Cash build, no problem. Part of a home isn't an asset to be able to secure a loan. You would need to assure the bank that the home can be built in a timely manner, up to certain standards, and appraise for a certain amount once completed. They may require more than the standard 20% down to secure a owner builder loan. Your budget is unrealistically low, even with you doing some of the labor.

I agree: Cash build, no problem. Half-finished house that the bank can't re-sell easily. Done by amateur labor, which the bank can't know will be quality, the answer's almost certainly no.

I could see this working ONLY IF you have a substantial asset (i.e., land, a business) that you could put up as collateral.

I disagree with the idea that the budget is unrealistically low for the shell of a 1300 sf home. That's quite small, and if it's a simple floor plan completed with builder-grade materials in a low cost of living area, it's possible.