Mortgage applications require a 2-year history of employment, income, and living history.
When you do not have a 2-year employment history it can still qualify as long as the employment and income is likely to continue. One way to prove that is if you have recently graduated school (like college, or a professional trade school) and have begun work in a field associated with what you studied for, then that can substitute for the 2-year employment requirement. Another is if you have returned from an extended absence from the work force, and there was a 2-year history of employment prior to the absence. Still even if those two situations do not describe your employment it may be possible to qualify in other ways, depending on the overall employment situation (for example if your income is salaried then that is much stronger than being on commissions).
A 620 credit score can qualify these days with more and more lenders (credit is easing up), however what delinquencies & late payments are on your credit report that brings the scores down to a 620 level is equally as important as the scores themselves. With a 620 score a lot of underwriters will apply extra scrutiny to your mortgage application, for easier time qualifying, and many more lenders to choose from, I recommend you aim for 640-660 scores. If you have at least 3 or so months until you'd be buying then it's possible to get your scores What is on your credit that is bringing your scores down?