It is a state program so can vary, but no, you usually qualify for medicaid based on your income on the day you apply. If you lose your job on July 1, you can qualify even if you’ve already earned more in the year than would be allowed.
My friend’s brother was taken to the hospital on July 4. We don’t even know how much he had earned that year (or withdrawn from his 401k) and he qualified immediately. (We are in an expanded medicaid state)