Meta recruiter said he would reconnect with me next month. Realistically, how much time does that give me to study?
What time in the next month? There's a big difference between early August and end of August. I recommend reaching out to them to clarify: https://www.jointaro.com/course/ace-your-tech-interview-and-get-a-job-as-a-software-engineer/talk-to-your-recruiter/
What I will say is that unlike most companies, Meta does central hiring where they just hire qualified people into a big pool and then dole out those engineers into teams after they pass the interview. Historically, this has been through bootcamp but I heard that Meta is more like Google now where team matching happens around the offer stage.
The difference between central hiring and targeted hiring is that there's generally more leeway to postpone the interview as there isn't individual pressure to fulfill a headcount. So if you need more time, just take it. If Meta is interviewing you for E5, then they should be accommodating.