Pre-approval stalls for boring reasons. Documents arrive in fragments, a credit report has an error nobody checked, or a large deposit turns up with no explanation attached. Two weeks of preparation removes most of it.
Week one is paperwork. Pull your credit reports and dispute anything wrong, because corrections take weeks and cannot be rushed later. Gather two recent pay stubs, two years of W-2s or tax returns with all schedules, and two months of statements for every account you hold. Write a one-line explanation for any deposit that is not payroll, because you will be asked about it anyway.
Week two is decisions. Work out what monthly payment you actually want, which is usually below the maximum any calculator will hand you. Decide how much cash you are willing to part with at closing, and keep a reserve behind it. Then read up on the programs you may qualify for so that the conversation about them is a check rather than an education.
Timelines vary by lender, by program, and mostly by how complete the file is when it arrives. What you control is the completeness. Send everything once rather than in pieces.
The affordability calculator at /mortgage-calculator/affordability/ is a reasonable place to settle on your own target payment before anyone else suggests one.