In that sense it's like buying stock. You don't have a taxable event for buying it, but you do want to keep track of the purchase price (which the exchange should do for you). When you use or sell the coin is when the taxability comes into play. Whether it is a cash-out into fiat or if it is using crypto to purchase something or pay for a service, that's when a taxable event has occurred. If you didn't exchange, sell, or use your purchased crypto in 2020, (only purchased or held), there's nothing to report (although you still want to answer yes to the crypto question in the return). This Help Article has more detail: How is cryptocurrency like Bitcoin taxed?
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