It's a tricky one, isn't it?
Well, you are not the only one and there are even some Czechs (including me :D) who can't get the twist of it either.
'Rž' is kinda, kinda similar. Just try to say it at the same time. Note that r in Czech is trilled, so if you can't pronounce it, I suggest you start with that.
You may wish to check how it should sound on Forvo: https://forvo.com/word/cs/%C5%99/ and there are surely some videos on YouTube. Here are some tips as well: https://www.quora.com/How-is-the-Czech-%C5%99-pronounced
And don't forget this tongue twister: Třistatřiatřicet stříbrných stříkaček stříkalo přes třistatřiatřicet stříbrných střech. ;)
BTW: Have a lingot for your great question and impressive streak :)
Thank you very much. I like how not even the native speakers on Forvo seem to agree on how to pronounce ř. The sound samples sound like at least three different sounds to me.
Btw, my coworker's native language is Czech and I will definitely welcome him with the sentence "Třistatřiatřicet stříbrných stříkaček stříkalo přes třistatřiatřicet stříbrných střech" on Monday :D