That $2,000 is cash at closing. It shows on the settlement statement as a charge to you and you wire it with everything else. It doesn't get added to the loan amount.
The reason people think it can be financed is that seller concessions look like financing from the buyer's side. If the seller agrees to credit $4,000 toward your costs, you effectively borrowed that money by paying $4,000 more for the house and borrowing against the higher price. That works only up to the concession cap for your loan product, and the caps differ by loan type and down payment size. Lenders also won't let a concession exceed your actual closing costs, so you can't turn spare concession into cash back. Confirm the cap in writing with your lender before you write the offer, because the numbers change and they vary by program.
So the honest cash line for your sketch is down payment, plus closing costs, plus whatever slice of your agent's fee the seller doesn't cover, plus your reserve. On a $200,000 purchase with 20% down that's $40,000, roughly $4,000 to $6,000 in closing costs depending on your state's transfer taxes and title practice, and then the agent gap.
One piece people skip on a first rental: the property needs cash after closing, not just at it. A vacant unit that needs paint and a lock change and a first month with no rent is real money, and it lands in the same 30 day window as everything else. Budget it separately from the acquisition number so it doesn't get absorbed by an inspection surprise.