Can I say a work trip is unaffordable when the expenses will be reimbursed?

The hotel quote came to $360. My manager said, "Submit it afterwards. You get all of it back."

The two-night trip is for work, and the hotel has been approved under our team's expenses process. Reimbursement usually takes about three weeks after a claim is submitted. I have $700 available until payday, with $260 already needed for bills and about $80 for groceries. Paying for the hotel would use the rest.

I'm new to the team and everyone else seems to book without discussing their bank balance. I could move money from a separate savings pot, but I'm uncomfortable making that the normal way work travel happens. I also don't want my manager to think I'm questioning whether the company will pay me back.

Would you say, "I can travel, but I can't front this booking," and ask whether the company can pay directly? Or is it more reasonable to use my savings this time and raise the process later? The money comes back eventually; it's the three weeks in between that I can't make feel free.