[Tijeras_Slim]

The Little Boy gun-type weapon is a great deal easier to build than the Fat-Man implosion device. The biggest hurdle was enriching the uranium (which is still the problem, unless you can obtain some that is already existant). As far as the design science of the device is concerned, as long as you weren't particularly interested in miniturization of optomizing yield, a reasonable competent physicist could get it to go pop.

[Timesink]

As I recall, they never even tested Little Boy. Dropping it on Hiroshima was the test; that's how certain they were that it would work.