Conditional approval (urgent)

I’m no longer able to stay in my current place of living and only have 30 days to get out. I applied to an apartment and they gave me conditional approval. Then they just asked for proof of social and photo id. They said because of my credit score they don’t need to see income.Does this mean I’m pretty much good? Don’t wanna waste money on more application fees because I don’t have a ton of time to save for the move. But should I still keep applying places ?