Is it a valid noun "the built"?

Solution 1:

In your example, built is a nominalised adjective: https://en.wikipedia.org/wiki/Nominalized_adjective

The most common appearance of the nominalized adjective in English is when an adjective is used to indicate a collective group. This happens in the case where a phrase such as the poor people becomes the poor. The adjective poor is nominalized, and the noun people disappears. ...

Thus we have

"The odd" = The numbers that are not even (or the people or things that are abnormal, etc.)

"The lame" = the lame people or lame animals.

"The built" = the built structures.

Another case is when an adjective is used to denote a single object with the property, as in "you take the long route, and I'll take the short". Here the short stands for "the short route".