file in 2021 for tax year 2020).
The IRS Form 709-Gift Tax Return is really not a "return" of any type in any way, form or fashion. It is only a "report". It's not filed with any income tax return and you don't have to wait until tax filing time. She can complete and mail the 709 "right now" if she wants, and be done with it. As you said, nobody will pay any taxes on it - at least not a "gift tax". That money your mother gave you, she probably already paid taxes on in a prior year anyway - or at least a vast percentage of it.
Overall though, she might want to wait until your mortgate is approved and you have closed on the purchase. Having the down payment is no guarantee the loan will be approved.