This is “frowned upon”, but some mortgage lenders can work with that, although they will require extensive documentation, proof of income, and may also require other proof (letters from your landlord, from your insurance company, … showing that you’ve been paying on time). You’ll also probably have a higher rate. If you’ve been banking with your bank for sometime, I’d recommend you start here, otherwise, a good mortgage broker (not all of them will know how to deal with that) may help.

FYI, while you don’t have a credit card, some other companies do report to credit bureaus, for example some utilities, cellphone or internet providers. It may be worth it to check if you have a credit file with Transunion and Equifax: you can either request your credit for free on their website (warning: their process is convoluted so they’ll try to sell you their service quite a few times) or through apps like Borrowell and Credit Karma.

Regardless, having a good credit history makes things simpler by standardizing them.