When Should I Start Applying

I am a LPN who will graduate with my BSN the first week of May (whoohoo!). I do want to change employers as I am currently working in private duty and hope to get back into an acute care setting. My question: when should I start submitting applications/resumes? Can I now or do I have to wait until I have my license? Thanks in advance for advice!
Now, when I was in school for my ADN, we started in March. It can be a process. Most facilities are looking now with knowledge that they will have to wait until you pass NCLEX.

Right now. I had my first interviews in the March before I graduated.