tips for Assistant Professors applying for new Assistant Professor positions after being cut
You are being let go for a reason that apparently has nothing whatsoever to do with your individual performance; your program was cut, and you as the (most?) junior person, are being let go first.  That should not be interpreted as a reflection on you personally, or the quality of your work.  Everyone in academia knows that things can be unusually difficult right now, and people are losing jobs that would have been totally secure under normal conditions.  Of course, you will need to explain why your position has gone away in your application package, and your recommenders can explain it was well.
Actually, the kind of recommenders you have available in this situation could potentially give you a significant advantage, relative to other applicants for the same positions.  You already have experience working as a full-time (possibly tenure-track) faculty member, and you should get a senior person in your department (the department chair being the most natural choice) to write a letter on your behalf that talks not just about the quality of your research, but also addresses your capability as a teacher in a full-time faculty position and your service work.  A chair's detailed recommendation that says that they are extremely unhappy about losing you, due to budgeting changes completely beyond your control, could be very compelling to hiring committees.
All this being said, given the current economic situation, you are probably going to be in for a rough ride.  In fields where whole majors are being cut, there are likely to be few new jobs opening up, so competition is likely to be extremely fierce, even for people who already have faculty experience.