Peter wrote this to Christians who were scattered and suffering, people with real reasons to be anxious. So this is not a naive verse from someone with an easy life. It comes to people already under pressure.
Look at the line right before it: humble yourselves under God’s mighty hand. Casting your care on Him is an act of humility. It is admitting you were never strong enough to carry this alone, and you were never meant to be.
And notice it says give ALL your worries, not just the presentable ones. The picture is throwing a heavy pack off your own back onto Someone stronger. The reason is the part that undoes you: because He cares about you. Your anxiety is not an annoyance to God. It is His concern.
So tonight, name the specific thing and hand it over out loud. When it climbs back onto your shoulders in an hour, hand it over again. This was never one and done. It is a daily casting.