Not impossible, just extremely difficult. I'm a ham and getting some contacts over moonbounce is a personal goal of mine. Historically this kind of thing has required some pretty large antenna arrays and very high power though:
Isn't there a moon bounce mode in WSJT (or one of those digital modes) that provides enough coding gain that 100W and a single large Yagi is enough? I seem to recall hearing something like that... but, yeah, on CW a monster antenna and the legal limit of 1500W seems to be the median system.
A long time ago I started collecting parts for a 432MHz EME system. Life got in the way and I never built it out. Good luck with your endeavor!
> but, yeah, on CW a monster antenna and the legal limit of 1500W seems to be the median system.
A good ten years ago or more, they used Arecibo to transmit CW moonbounce on 70cm. I was able to receive it in my back garden with a handheld and an 11-element Yagi balanced on my clothesline ;-)
https://hamradio.engineering/eme-moonbounce-bouncing-signals...
http://www.g4ztr.co.uk/app/download/13284489/RaCcom_Feb14+EM...
http://www.g4ztr.co.uk/app/download/13300096/Radcom_Mar144+E...