A child without a wand is like a child without a pencil. They can always borrow one, even if the borrowed pencil wouldn't be as good as their own if they had one. Now replace the word pencil with the word wand. There are multiple solutions for this, although they are purely canon-based speculation because there are no recorded cases of this. However, all of the possible solutions do have evidence/examples, and in some cases, quotes to back up their likeliness and reliability.
Theory 1: He would probably just make a custom wand based on which ones produced a better result, even if it is not a perfect one. For example, if a person did not have a perfect result with Applewood, but it had a better result than some other wand wood, then Ollivander would custom-make an Applewood wand but just change the core up a little bit. I do have a quote to support this, from the Sorcerer's stone, from when Harry had to try many wands until he found his match.
"But the more wands he tried, the more excited Ollivander seemed to get..."
This supports that Ollivander would have been happy to provide a blossoming witch/wizard in the making with all the tools that they would need because he really seems to love what he does.
Theory 2: They could choose a wand that felt, "friendlier in his hand," (DH1 quote) that worked decently for that witch/wizard, similar to the way Hermione and Draco's wands both worked reasonably well for Harry.
Theory 3: They could try their luck with another wandmaker if no Ollivander wand seems to work. Ollivander only uses the "3 supreme cores," suitable for wands, so it is possible that they would need an untraditional core as well.
See this link for the "3 supreme cores".