The down payment amount stated in the offer letter does not have to be the same as the down payment amount you end up making. You are not asked for proof of funds when you submit the offer.
E.g. if you’re making an offer for 600K and you’re concerned that your 10% down payment would make you look weak, you could write “deposit 6K, loan 417K, down payment 177K”. You may not even have 177K. When the offer is accepted, you run the numbers and make the down payment that is appropriate for the situation.
