Making offers without a pre-approval letter is dicey, although it doesn't appear to be necessary (full disclosure, when purchasing my first home, I personally treated it as a necessity).
If I was in your position, I'd likely try to pursue a means of funding first before deal hunting too aggressively. Here's how I'd approach it:
1. Exhaust available solutions within the scope of your current earnings/lifestyle:
- Are you talking to a loan officer or a mortgage broker? Talking to a mortgage broker might allow you to get more creative with funding options.
- Have you looked into FHA loans at all?
- Are you interested in pursuing a hard money loan?
2. If your sources of income continue to be an issue, press pause on the property search altogether and look to make a shift into more conventional sources of income (or otherwise regulate your income in some fashion)
- What this shift entails is a completely different issue - for example, if lenders would like to see a higher earnings level, this is a different question than seeing steadier/more regular earnings
Obviously I don't know the full context around your earnings situation, which is why bullet point #2 is extra light and only comes after exhausting other available options within the scope of your current lifestyle.