@Barbara3746. Trust is a two way street. Ask them to complete their profile first before you tell them anything and have a set of questions you would normally ask eg what is the purpose of your stay, have they used other platforms before so you can see their reviews, details of all guests in the booking, reaffirm if they have read the listing etc etc.
By now they will have either given up or be on the way to you feeling more comfortable as a potential guest.
But @Joan2709 is right, a month is way too long to risk if you need to get rid of them. I have done a couple of first timers for a weekend but never a week or longer and they all get the same questions. I'd say half give up but at least I have responded quickly, which is important for Superhost stats.
Good luck 🙂