A mortgage is not a requirement to building a house, but making that tradeoff will induce a number of constraints and require non-standard ways of living for a while that may be more than you or your family find acceptable. The main ones are being uncomfortable in the short term, and probably living in a rural setting where land is less expensive.

Here is a link to a book that lays out a very good strategy:

https://books.google.ca/books/about/Mortgage_Free.html?id=U8...

(warning: although I read this book and considered it's approach, I used a slightly different strategy towards home ownership without a mortgage that allowed me to purchase existing homes)