You pay interest that has accrued for the prior month and anything left from the payment is applied to principal Paying ‘early’ is fine as student loans are simple interest so if you pay on the 10th of October, it will pay 30 days of interest from Sept, and then 10 for October. If you then pay on Nov 10, you’ll pay 31 days of interest and the rest will be applied to principal.
Wasn’t your daughter in school when Covid hit? She may still be in her 6 month grace period so the servicer would not send a bill yet. You can always start paying and thus pay down any interest that accrued while she was in college before it is compounded into the main loan. It will consolidate interest only once before the payment schedule is established, but after that it is simple interest, with the payment applied to accrued interest first, then principal.