Odds are that your timeline is working out fine.
You can look up the wait time for a visa interview at your nearest US consulate here: https://travel.state.gov/content/travel/en/us-visas/visa-information-resources/wait-times.html
The wait time for the interview is the major hold-up. It’s less than 2 weeks at most consulates, but it can be several months long in a few instances. Most visa applicants will see their visas issued within a week of their interview, or rejected on the spot at the end of the interview.
A comparatively small number of visa applicants will have to endure administrative processing. Administrative processing means that the US government needs to run additional checks before deciding whether you qualify for a visa. That may happen because you have the same name as someone on a US government watch list (probably a different person with the same name, but they need time to double-check that), because you are a close relative of a government official and the decision on your visa application has diplomatic implications, or because you want to study a major that may expose you to sensitive technologies (e.g. with military applications), like some graduate engineering programs.
The US government strives to resolve cases of administrative processing within 90 days of the interview. That’s the main reason why it makes sense to apply for a US visa as early as possible. But to re-iterate, comparatively few visa applications necessitate administrative processing and odds are that it won’t affect you.