There is a lot that goes into a credit score — and not very much that can be done instantly. So much depends on longevity of credit, payment history, and length of time at a residence. So if they have additional outstanding credit (besides the car loan) the first step would be to pay down those balances. Being current on all outstanding debt is critical to offsetting those longer-term things.
That score isn’t bad for young people — assuming they EACH have a score in the 700s. They probably hadn’t had time to build a credit history. But do they each also have student loans? When it comes to getting a mortgage, other debt matters — a lot! And have they saved enough for a down payment?
Also, have they looked into “first-time home buyers” programs (in Illinois at www.IHDA.org).
And have they checked at banks like Wintrust or online at Rocket Mortgage to see4 how much of a monthly payment or total home price they could afford?
Finally, a bit of unsolicited advice. If they buy a home together BEFORE they are married, they should have a legal agreement about how they will share the mortgage and insurance expenses — and whether one has the right (assuming the ability) to buy out the other in case of a split.