My mother had a reverse mortgage, How can I finance without probate?

You likely cannot. A lender is not going to lend to you on a property that you do not own, so the property will have to go through probate to transfer title to you in order to be able to get a loan on it. Sorry I don't have better news.

Unless you are on title, or the property is in a Trust of which you are the trustee, you cannot refinance without a probate. You are not the legal owner and will not be until/unless it is distributed to you by court order or Trust.

I think you are mixing apples and oranges. If you want to purchase, then you could try to get financing to buy your mother's home independent of the reverse mortgage. But if your mother died with no will, then you might look at transferring title to the house to you via probate. If there is no equity, then ignore the probate process and just purchase it outright from the title holder.