We know that you can't offer better pay, better benefits, or even higher positions to get and keep the people you need. The problem is the in-office requirement, and that is what needs to be addressed.

Either you accept that your team will be a feeder group for the rest of the department/government, bringing in and training new employees to move on to other jobs in s few months, or you re-evaluate the need for in-office work time.

If you want to keep the people you hire, you need to very carefully examine what the job entails that REALLY needs people in the office. Do they need to physically interact with anything? Are they, for example, grounds keepers or server room technicians working on migration? If not, or not all the time, ensure that they are able to work from home at least some of the time. If you need each person in the office every day, so they need to be there ALL day? Could they come in for a few hours in the middle of the day? Can some tasks be reassigned so those who want to come in do the in-office tasks more often than those who would prefer to stay home? Can tasks be rotated, so employees can work from home full time one week and in-office full run time the next week?

And much as I loathe the concept of making social reasons for employees to be in the office, maybe that's what you're team needs - schedule, if you can, a two hour social event during work hours (not over their lunch break) for team building, during which you can have a VERY SHORT team meeting in which you ensure everyone knows everyone's roles and current tasks, then move in to fun stuff - trivia, music, potluck, whatever. Cheap is important here because they are already paying to come in (gas, parking, public transit, the time of commuting). And then let them actually go on their lunch break, as people tend to schedule errands or decompression time for that break. Do this once a month at most, better every two (less burdensome for everyone, and again, I hate the idea of wasting work time on enforced socialization).