No there is no way you can buy Ethereum at the moment and avoid the high transaction fee except you want to take the risk of leaving it on the exchange. But if you wish to transfer it to your personal wallet you will need to pay high fees which comes as a result of the congestion on the Ethereum network. The fee at $7 is even lower when compared to last week that it was above $20. If it is not much of a high fund I will advise you leave it off for the moment.

You can make use of other layer 2 blockchains like Solana, Arbitrium and polygon for other payment transactions.