I don't have a US tax number yet and I'm selling — does FIRPTA filing just stop?

The sale and the withholding do not pause because you lack a taxpayer identification number. The buyer must still file Forms 8288 and 8288-A and remit the tax on the normal timeline even if your TIN is missing. So the money goes to the IRS as scheduled. What stalls is the part that matters to you: the IRS will not issue the stamped seller's copy of Form 8288-A until a valid TIN is supplied. Without that stamped copy, you have nothing to attach to a return to claim the withholding back.

The buyer's compliance is satisfied by filing and remitting. The gap lands on the seller, because the withholding sits with the IRS effectively unmatched to you until your number exists. The practical consequence is a delayed credit: you cannot file a clean US return claiming the withheld amount, and you cannot get a refund of any over-withholding, until you have both the number and the stamped statement.

A nonresident individual who needs a number applies on Form W-7 for an ITIN. Helpfully, the W-7 can generally be submitted together with the Form 8288-B withholding-certificate package, so a seller who is already pursuing reduced withholding can solve the TIN problem in the same filing rather than as a separate slow step. If you are not filing an 8288-B, you still pursue the ITIN so the stamped 8288-A can issue and you can claim the credit. The number is also a prerequisite for any later return work, and it ties into other foreign-seller filings such as the estate-tax analysis in /guides/form-706na-estate-tax-nra.