So it's quite possible that the online Magic game manipulates the deck. Keeps players engaged more so they make more money. Pretty standard these days; Candy Crush famously does this too. Looks random, but very much isn't.
The game mitigates this with a mulligan rule, where you can get another hand with one less card if you want. That way, you can get rid of a bad hand, but it costs a card each time. Commonly, magic players overvalue the card, and don't mulligan hands that they should, but it is also possible (and common) to just lose games to luck even if you do everything right - top MTG pros only have ~65-70% win rates against random people.
MTG arena apparently also does an internal free mulligan for you (to make the game more fun) - it draws 2 hands initially and gives you the one with the better mix of cards.