You should always check gas fee before make a transaction. You can check ETH gas fee here
https://etherscan.io/gastracker.
This is the pick hour. ETH gas price is less on 4-6 Am (UTC 0). If you do the transaction at that time, you can do the transaction at a much lower fee.
You are right, depending on the time zone, you can catch the moment when the price of gas is cheaper, in my region it is earlier in the morning. A couple of times I had to get up early in the morning to send several transactions, since the prices are just crazy during the day.