Have you pulled your credit to see if you even have credit scores now? If you do (and there’s old positive, but little/no negative credit activity shown on the report) you may well be fine. You’re right that establishing a credit history in two months is unlikely to happen. Accounts are shown for 7 years from the date of last activity, so even if you’ve been on a cash basis for the past 5, it’s possible you still have scores. Congrats on your income/assets, and rental payment history.
There are non conforming (aka: portfolio) loans that you more than likely could obtain, albeit at higher rates and typically not 30 year fixed loans. I’d start by pulling your own credit report at the government mandated website annualcreditreport.com It won’t show your scores, but will show all account activity being reported by the credit bureaus. Pull all three bureaus to see what shows up.
If you have any further questions, I’d be glad to help, I write loans nationally. Thanks, Ted