The Corps of Engineers is in the business of letting and administering construction contracts. The Corps of Engineers will not use troops to do the construction.
So far as the COE is concerned, administering a contract for a border wall is not a lot different than a contract for a river lock or dredging a harbor
Just do it and get it done.
..... What’s to keep the currently re-spawning Swamp from scuttling this idea?
And not at all as engineer-heavy as building a missile silo; although arguably more pertinent in today's environment.
COE could do it with minimal effort. By using competitive-bid, multiple regional prime contractors who were familiar with local conditions together with on-site 24/7 COE inspectors it essentially would be an accelerated project without the typical costs. It could be scheduled at a pace consistent with the Pentagon's (prudent) release of funds.
(Imagine a number of concurrent 60-90 day projects...bingo!)
If the CinC did not allow this national defense project to be halted by some leftist federal judge, it could be completed so quickly it is unlikely the anti-American border crowd would have time to effectively interfere.