On one of his first official tours through the new Sydney Modern, after roughly a decade developing the project as director of the Art Gallery of New South Wales, Michael Brand highlighted a few signature pieces: a new commission by an Aboriginal artist using found metal; an immersive sculpture, first exhibited in Seoul, that visitors create by rolling balls of clay; and a giant video from a New Zealander, imagining Oceania without people of European descent.

But at each stop Sydney’s natural surroundings beckoned. State officials following Brand — after forking over most of the museum’s $230 million in construction costs — praised the views more than the art. The new free-standing building, designed by Sanaa, Japan’s Pritzker-prize-winning architects, also seemed unsure of what to show off, with walls of glass opening up to Sydney’s big blue sky and shimmering harbor.

“The in-between spaces are as important as the gallery spaces,” said Brand, as he stood in the wide open middle of the structure.

“It’s a museum and a building that can only be in Sydney,” he added. “Both through our collection and through the architecture.”

Dozens of cities have tried to create their own marriages of art, architecture and landscape as part of a global museum building boom that began in the ’90s with Frank Gehry’s Guggenheim in Bilbao. The new Whitney, with its huge floor-to-ceiling views of the High Line and the Hudson River, and the Louvre’s new Arabic-galactic outpost in Abu Dhabi, on the edge of the Persian Gulf, are among the latest prominent additions.

But the Sydney Modern, which doubles the exhibition space of the Art Gallery of New South Wales, one of Australia’s most important art institutions, faces an especially acute cultural challenge. Museum building in a real-estate obsessed city that Mark Twain called “superbly beautiful” — in the sunny heart of a proud “sporting nation” — often requires overcoming a barrage of negativity. The Sydney Opera House was loathed before it was loved, and the Modern has traveled a rough road already.

Some critics, including a former prime minister, have been condemning the project from the very beginning, mostly for grabbing valuable green space. Others have taken to calling the completed building, which opened on Dec. 3, an ugly and expensive set of boxes stacked on a stunning hillside.

Echoing a common refrain, Judith White, an artist and former head of the Art Gallery Society, the gallery’s nonprofit membership arm, said a harbor view through glass is a step down. “It’s what corporate offices and the homes of the wealthy have,” she said.

The project’s price tag is far from exorbitant — it’s in line with average costs per square meter for cultural infrastructure in the region, according to AEA Consulting, a global strategy and planning firm. But Sydney’s elites, said Ross Gibson, a professor of Creative and Cultural Research at the University of Canberra, have a long history of underinvesting in cultural ambition while demanding quantifiable returns.

“Most of the rulers and commentators really do believe that ‘culture’ is a nonessential or luxury additive rather than part of the educational, civic, ethical and moral systems whereby a society might govern its core values and activities,” he said.

In practice, Brand and his team say they want to balance a respect for traditional Sydney with a touch of provocation.

They know their shiny newcomer of a museum must satisfy staid officials first: admission is free; the state of New South Wales covers the gallery’s operating budget. But the expansion, coupled with curatorial overhauls in the older building, also aims to make people see Australia’s largest city with fresh eyes — as a cultural hub with deep Indigenous roots and close ties to its Asian neighbors, looking less to Europe or America for validation.

Brand, an Australian art historian who previously served as director of the J. Paul Getty Museum in Los Angeles, calls the complex, with its new building, “a continuation of Sydney.” For its early adopter fans, the Modern represents something far more jarring and worth celebrating.

Around 120,000 people visited in its first 10 days, according to the Gallery’s tally. On two recent mornings, there were moments of where-do-I-go confusion, but for the most part, visitors praised the serendipity of the art, and the indoor and outdoor experiences, where sculptures provided seating or shade and a cafe sold striped raspberry croissants and perfect espresso.

“It’s so open, it’s so welcoming, it feels like a playground,” said David Galafassi, 44, a doctor and a musician who had come for the day with his family. “It’s all the things that we’ve been missing.”

The new addition is certainly distinct from the museum’s original neoclassical building, finished in 1909, which sits next door. Shorter in stature, with no grand facade, the Modern’s first impression is almost airport-like — a square of glass with a metal ceiling.

Inside, there’s more warmth and fluidity. The entry’s design points to the Yiribana Gallery of Aboriginal art, which has been elevated from a lower floor of the original building, and it offers an expansive view of landscaped terraces and sloping walkways. The pinkish, speckled concrete floor curves slightly downward, toward the galleries.

“The slope invites you in,” Brand told me.

Many of the curators acknowledged that like the slope itself, they are trying to nudge visitors toward a less rigid experience. The first exhibitions mostly provide a sampling of the gallery’s collection, under a guiding principal of ignoring strict chronology and putting international and Australian art together in spaces that encourage meandering.

In an exhibition titled “Dreamhome,” a rounded-room installation with colorful beaded artwork and chairs from the American artist Jeffrey Gibson, a member of the Mississippi Band of Choctaw Indians and of Cherokee descent, sits within a few steps of three bright paintings from John Prince Siddon, a Walmajarri artist from the Great Sandy Desert of Western Australia. Next to those, Ramesh Mario Nithiyendran, an Australian artist of Sri Lankan descent, has contributed a floor-to-ceiling stack of eerie 3-D creatures meant to inhabit an imaginary apartment block.

Another exhibition space nearby — without an overarching theme — simply presents First Nations artists, like Roy Wiggan, a Bardi elder, near international giants, like the American painter Cy Twombly, and newer stars, such as the Korean conceptual artist Kimsooja.

Right angles in all the exhibition spaces are rare; interior walls create unexpected nooks, with darkness here, a sudden burst of sun there, and less explicit direction for where to look first.

The Sydney Morning Herald’s art critic, John McDonald, questioned the logic of abandoning “obvious taxonomies.”

“One of the abiding policies of Sydney Modern seems to be that Australian and international art are to be promiscuously intermingled at every opportunity,” he wrote.

Maud Page, the director of collections, countered that the goal was “a layering that then prompts people to question more.” And the building, she added, clearly helps.

The original design from Sanaa — which has a reputation for architecture that avoids intimidation, and includes the New Museum in Manhattan — has been altered to bend, literally in some cases, toward Sydney’s very particular surroundings and the Gallery’s eclecticism.

Just past the middle floor’s atrium, for example, a path outside leads to “Spirit House,” a Buddhism-inspired artwork (by the Taiwanese American artist, Lee Mingwei) built into the rammed-earth wall of the building.

The museum’s most striking experience to date also comes from what preceded construction, and what has been incorporated from below: a World War II oil tank, which has been turned into a subterranean gallery. Upon discovering it, Kazuyo Sejima, one of Sanaa’s two lead architects, called it a treasure.

The fact that the buried space was overlooked for years, but worthy of deeper contemplation — that seemed to perfectly match what Sanaa and the Modern were seeking.

She and her principal partner, Ryue Nishizawa, built an understated spiral staircase for entry.

The first piece to inhabit the tank, Adrián Villar Rojas’s “The End of Imagination,” defies time and the usual rules of museum interaction, featuring mammoth sculptures that can only be seen when lights from above move in the right direction. Darkness and the scent of industry fill the space until, suddenly, the artist’s craggy constructions that speak to climate change, destruction and possible rebirth emerge from the shadows.

“It’s not a human centric gaze,” said Villar Rojas. “It’s a place where you don’t make decisions as a visitor. You can be like, ‘OK, I want to go this way,’ but maybe the lights will tell you something else.”

Brand, the director, sitting in his office overlooking an unfinished Indigenous garden installation that is the final piece of the Modern’s puzzle, called the Tank and “End of Imagination” the perfect complement to what the Gallery hopes to create.

“There’s light, there’s landscape, there’s deep immersion,” he said. “That’s what I’ve always had in mind for us to do.” He paused as Sydney’s summer sun brightened the room. “I just hope everybody sees that.”