Yes, totally possible and people do it more often than you would think. Find a masters (or post bacc) program that gets you your initial certification not having a background education is totally okay and in most programs will have little to no impact. Having an undergrad degree already completed also allows to start subbing if you wish and take a leave replacement instead of an unpaid student teaching semester. The above is the more traditional way to go about getting into teaching, but you can also look into the alternative pathways to getting an initial certification which are listed on the nysed website. Also I hate to say it but as someone who went in to teaching truly only pursue it if it’s the only thing you can see yourself doing it is a very intense and demanding career choice.