I’ve read the Bigger Pockets book on long-distance real estate and am eager to get the ball rolling. 

I have 2 options:- finance the construction pre-selling the apt, and take my profits (expected to be around 700K pre-tax); or- finance the construction with a 6-7%/year loan (collateral = my house), keep the 10 units, and once the building is completed in 24 months, rent them for circa 180K/ year gross.

If you discovered the issue before paying for the appraisal that could hopefully save some costs (in case the appraiser is with the wrong AMC).Pre-vetting with the lender on rental history/AIRbnb/1007 as well as seasoning could help. 

I am about to graduate college in May 2025, and will be making about $120k (pre tax) in my full time job postgrad (Washington DC area).

Is there a pre existing loan with that bank with either of you?

I would recommend that you get out to local meetup events, as that is where you will make the really deep connections to help you get rolling. 

Is there a specific duration I should be pre-approving an inquiry within?

However, if you feel you need their input earlier, you could offer to pay for their visit to walk the property with you pre-inspection.

After 4-5-6 years then maybe roll them up into a small mulitfamily.Another option if you have the credit and some capital is to buy a 4 unit as owner/occupied and live in one and rent the other 3. 

Quote from @Miguel Garcia: If I look into investing out of state should I look to get pre approved by a lender in that area or would a lender in my area be fine?