The time of financing is going to depend on a few things...
1) How do you plan to write your offers? If your marketing strategy is a QUICK close with sellers, you can't go the DSCR route. Best case scenario these loans will close in 20 days (if all the stars align), in reality they average 30 days.
2) I understand the end goal is LTR but if you're calling eviction records, auctions, craigslist, etc chances these homes are going to need a rehab component. Not to say this is always the case, but if someone is being evicted chances are they are not maintaining their home. If you plan to rehab, rent, and refi then a HML or PL (same thing, really) is a good option.
3) The last piece I would mention is to line up your capital now. If you plan to pull on equity, aka HELOC, you're looking at around 30 days. Obviously pulling on the 401k will be faster, but that may come with some tax disadvantages.
The good news is that whether it's DSCR/HML/PL no one should be pulling your credit upfront or taking deposits. You can get a preliminary approval with soft quotes then once you have a property under contract and start the loan process you can approve the credit pull.
Good luck with all of this. Feel free to shoot me a dm with any questions!