What’s the best timeframe to send a letter to the hiring manager after submitting your resume for an internal job application?
Do you know the hiring manager? If yes, send them a short email and let them know you submitted an application and would be happy to answer any questions.
Are you a strong candidate for the position or would it be a stretch role? If you're a strong candidate, they are likely to shortlist you anyway. If it's a stretch role, it's better to reach out early so they don't dismiss your application without serious consideration. If they get a number of strong candidates they might move quickly to cull out less obvious candidates.