One month isn't unreasonable. To speed up the process, try getting more warm intros: those work much better than handing out resume (even if it didn't work out for you the first time).

These can be low-level connections, e.g., reach out to 2nd or 3rd degree LinkedIn connections that work there, and ask for a phone call to talk about how they like the job. If you like the work, ask them to pass along your resume.