Some casinos don't have this minimum requirement for deposit but have it for withdrawal but if a casino have them for deposit then it will be on the lower level like $1 on most cases then if someone sent any lesser than that then I doubt the contact team will take time to resolve the matter, they will simply advice them to make another deposit that is higher than the minimum and it is the right thing to do.
Many casino do not combine your previous transaction even if you send extra amount to same address and meet your minimum.
So it is not advisable to send another transaction blindly now. You need to ask support with your TXID, amount, coin, network, sending address and deposit address if they can do any manual credit or refund. If you talk in live chat then even if they say top up again and meet your minimum, you should not do it without any written confirmation.
Ops could have done better to mentioned the casino involved and how much is their minimum deposit threshold and also he should tell us how much he sent in that is rejected as below minimum amount to deposit?
Also sending extra into the wallet with the hope that it get topped up with the first deposit is not also technically achievable as, each deposits will be treated as separate order, ops can contact the support and let him hear their own conclusions on this case some casino can refund your if such mistakes happens.