Altcoins popping up like in a game "whack a mole". Some did 50%, some did 5x. Is there any methods that could be used to predict which altcoin will be next? (I guess there must be some indicators, narrative and etc.) or it is purely random game?
It's tough to gauge the situation just by looking at the chart; you really need to stay updated with developments. If the projects have channels or communities, consider joining them to stay in the loop about upcoming news. Typically, during or just before an altcoin season, even a bit of positive news can quickly generate hype. So, it’s worth the effort to follow these developments closely. Otherwise, you might find yourself jumping on the wrong altcoin out of FOMO'd.
Why not just go for big alts and await their eventual pump?
The safest option for me would be to do that, IMO.
That is, if there is not need or goal to do otherwise.