This week is crunch time for the worst-hit Bay Area counties to ramp up efforts to bring vulnerable and infected homeless people into hotels and overflow shelters during the coronavirus crisis, and the verdict is: So far so good. Generally.

From Santa Clara County to Alameda and San Francisco counties, thousands of hotel rooms and temporary shelters are coming on line, and, thanks to a delay in the surge of COVID-19 cases that health experts had expected to begin statewide around now, they are nowhere near full yet.

Advocates in San Francisco say that’s because authorities are moving too slowly in bringing homeless people into the rooms, and that they need to escalate their efforts. But program planners around the region say they need to move methodically and leave some room for that surge — which now is anticipated for May.

“It seems that the mitigation steps we all put into place about physical distancing are having a positive effect, and brought a little breathing room,” said Ky Le, who runs the coronavirus homeless sheltering effort in Santa Clara County, which Tuesday had the greatest number of overall COVID-19 cases in the Bay Area at 1,285. “But we’re moving fast and will be adding a lot more beds now.”

In the past few days, Le secured the bulk of his county’s 338 shelter, hotel and trailer beds, and in the next two weeks he expects to add 556 more. They would have had more, but he had to spread out the original 624 beds he secured to reach that 338 baseline number with proper physical distancing.

“We’re not trying to move toward a specific number right now — we’re just trying to line up all the resources we can and manage the numbers when they start coming in heavily,” Le said.

That’s the strategy so far not just in the Bay Area, but the state as a whole. In mid-March, every health agency was bracing to be swamped with COVID-19 cases this week, but Gov. Gavin Newsom has said in the past few days that California’s surge will now likely come toward the middle of next month.

Newsom said Tuesday that in anticipation of that surge, he wants about half of the state’s 108,000 unsheltered homeless people put into properly spaced shelters, trailers or hotel rooms. The counties and cities are generating the bulk of those spaces with the help of $850 million in state homeless-aid funding, and Newsom has set an additional goal of state-funded hotel rooms at 15,000. So far he’s secured more than 7,600 of those.

Homeless people being routed into those rooms or beds must be vulnerable by age and underlying conditions, have been exposed to the coronavirus, or actually have the disease — and those guidelines are being followed by counties in the Bay Area as well as statewide. The Federal Emergency Management Agency is reimbursing the state and localities for 75% of the cost of the hotel rooms if they meet those parameters, but not for homeless people who don’t.

“Look, it’s a stretch goal,” Newsom said of bringing 50,000-plus homeless people inside. “No one’s naive. This is unprecedented. ... And there’s only so much that we can do from the state. We have to manifest this at the local level, and local partnerships are critical to make this happen.”

Aside from the humanitarian benefit of sheltering infected or at-risk homeless people, there is a bald economic incentive. A study led by University of Pennsylvania Professor Dennis Culhane and released late last month found that homeless people are four times more likely than the general public to need intensive care units if infected, and about three times more likely to die of the disease.

Chris Herring, a researcher on homelessness at UC Berkeley, pointed out that a typical stay in ICU costs about $73,000 a week as opposed to about $700 a week for the 4,500 hotel rooms San Francisco intends to rent to take in a mix of first responders, people from residential hotels and homeless folks. About half of those rooms have been secured — and city planners say they intend to adjust upward the target number of rooms as needed.

“You save lives, not to mention money, if you move people into hotels,” Herring said.

With that same desire in mind, a majority of the San Francisco Board of Supervisors on Tuesday introduced an emergency ordinance that would require the city to lease at least 7,000 hotel rooms by late April for homeless people not yet exposed to or infected by COVID-19. City planners say that many rooms would cost about $30 million a month including rent and the counseling, security and other services needed for many of the occupants. And with the city facing a $1 billion deficit, Mayor London Breed has resisted anything sweeping enough to put all homeless people inside, focusing instead on the most vulnerable.

“We all — from the city and the Emergency Operations Center to the advocates and people on the street — would like to house everybody, all the time, but that’s not happening right now,” said Emily Cohen, spokeswoman for the city Department of Homelessness and Supportive Housing. “I will say this, though. There is a level of urgency that I’ve never seen before, as there should be.”

In Alameda County, about 400 beds rented in two hotels with the state’s help for homeless people in the crisis had only about 60 people in them on Tuesday. The county is negotiating for several hundred more rooms in the next few weeks, said spokeswoman Jerri Randrup.

Contra Costa County was in the same situation, with about 300 beds now roped off and ready for use at auditoriums in Antioch and Richmond, said spokesman Will Harper. About 100 people from two shelters have been moved into a hotel to create physical spacing.

“We’re doing our best to prepare for the worst,” Harper said. “This is the first pandemic like this in 100 years, so we don’t know exactly what to expect.”

Kevin Fagan is a San Francisco Chronicle staff writer. Email: kfagan@sfchronicle.com Twitter: @KevinChron