I have a feeling that there may some confusion on definitions in this question.
When you say ARV, are you implying that the ARV, as in After-Rehab Value, is lower than the fair market value for the same property? Typically, the ARV and the fair market value are the same thing. If you're not getting some kind of discount from the fair market value, then there really isnt any reason to do any of what you're doing - just buy a turnkey property off the MLS and you'll have the exact same end result.
In other words, if the ARV of the property is $400k, then you shouldnt be getting a distressed property in need of rehab at $400k; you should be getting a completed, tenant-ready property for $400k. A distressed property with an ARV of $400k should be selling for much less than $400k, like $300k or less.
Typically, you would buy a distressed property with some kind of residential transition loan (RTL), with hard money being the most common type. This loan would cover both the purchase of the property as well as rehab costs. Once the rehab is complete and the property will appraise at fair market value (the ARV), then you would refinance into a permanent loan like a DSCR loan to payoff the hard money loan, as hard money loans typically have high rates and short tenors (9-12 months).
There are conforming renovation loan products that provide the funds for the acquisition and permanent financing as well as construction costs in one loan. This is what @Stephanie Medellin was referring to. The difference between these and hard money/DSCR loans are that these are still conventional loans - you still have to meet income and DTI requirements, cant close in an LLC, have to go through a conventional underwrite, etc. Nothing wrong with this, but this is not the same process as hard money or a DSCR loan.
Long story short, youre going to have two separate closings any time you use some kind of RTL loan for the purchase and construction financing, and another loan, like a DSCR, for the permanent financing. In some cases, if the same lender originates both loans, they may cut you a break on some of the lender fees, but youre still going to have 2 sets of title/attorney costs, have to get an updated lender's title policy, etc.
Based on what you initially described, if you're paying ARV for a distressed property, then the rehab costs should be funded out of what you've already paid for the property, and the loan that's used to purchase the property should be the only and final loan. In other words, if the ARV is $400k and the property needs $50k worth of rehab, then the $50k for the rehab should be paid out of the $400k used to purchase the property, not in addition to it. There wont be any bridge or construction loan; otherwise, you would be $450k into a property that is only worth $400k.