Although I've made profit with Bitcoin, at a rate I can't gain elsewhere, I prefer not to convince somebody to invest in it. Especially to somebody who still has suspicions or doesn't understand it yet, suggesting that he/she invests in Bitcoin could have a tragic ending. It could end your healthy relationship, too.
For me, it's better to just introduce Bitcoin and answer questions if he/she's interested about it. Let interest grow naturally. It's hard to give financial advice with a market that's highly uncertain. If Bitcoin suddenly nosedives, drops all the way back to $60,000 in the next week or two, and your cousin panics, distressed, and is losing sleep, won't even listen to you anymore, what would you do?
Yep, if we force our idea and they face a loss, then friendship could be broken over forced advice. Therefore, as a friend, I don't force anyone, unless I know the outcome and I convince my friends. And if they don't agree, I might make them a deal like I will cover some percentage of the loss or something just to make sure they invest, because true friends want their friends to grow.
But investing $ 20k directly is not good advice, but I can't say if it is because I need to know about the friend's financial status. If his friend's entire savings is $20k, then he should never invest it all in BTC.