Is it ok to apply to a job via staffing agency with a different recruiter?

I wasn’t sure how to title this, but can explain below.

I contacted a respectable staffing agency in my town and was essentially ghosted after a while, not sure why honestly as his last communication was that he had a job lined up that matched my skill set and interests.

Another job that peaked my interest showed up online, with another recruiter listed.

Is it alright if I apply for this specific job and don’t mention my initial recruiter?

I’d rather go through someone else and honestly need a new job, but don’t want to “burn bridges” with a potential firm that could help me get a new job. I have no desire to work with the recruiter that ghosted me, but don’t want anything to comeback and hurt me if it makes sense.

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