Once you’re in the Europa League, you’re just 15 games away from Champions League qualification for the following season. Those games can be incredibly tough. A side would have to deal with the group stages before potentially defeating Champions League-level opponents in the knockout phase, but it’s still within the realm of possibility.
It is difficult to imagine a mid-table Premier League side like Leicester City or Crystal Palace making the Champions League after winning the FA Cup in one season and then the Europa League in the following one. It may sound incredulous, but realistically it’s probably more likely to happen than one of those sides crashing the Champions League party at the top of the table.