As long as you submitted a 2018/2019 tax return, HMRC will use the information to assess your eligibility for the self-employed income support scheme. You don’t HAVE to have a full three years’ tax returns for them to look at, they’re just using three years to be able to average out profit for a more accurate grant figure (as self-employed income can vary wildly from year to year).
If your tax return was very low (because you worked a part tax year when you started out), this could mean you’re not likely to get much support from the SEISS grant. If you’re struggling with your income, register for Universal Credit. You can still work as a self-employed person if you’re receiving UC – you’ll report your monthly income and expenses, and any month you don’t earn enough you’ll receive a UC payment. The months where you earn more, you won’t get a UC payment, or it’ll be tapered. This taper is based on 63p less UC for every £1 you earn over the minimum allowance. (The allowance is different for each person, based on your circumstances).
Hope that helps!