auftauchen
to appear
To suddenly and often unexpectedly become visible or appear in a place.
Nach drei Jahren ist mein verschwundener Schlüssel plötzlich wieder aufgetaucht.
After three years, my missing key suddenly appeared again.

to appear / surface
Loading your saved state.
to appear
To suddenly and often unexpectedly become visible or appear in a place.
Nach drei Jahren ist mein verschwundener Schlüssel plötzlich wieder aufgetaucht.
After three years, my missing key suddenly appeared again.

'Auftauchen' is a separable verb. The prefix 'auf-' goes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Plötzlich tauchte eine alte Freundin auf der Party auf.
Suddenly an old friend appeared at the party.
The word consists of 'auf' and 'tauchen' (to dive). The literal meaning is 'to come to the surface'. This idea is also used metaphorically when problems or people unexpectedly come 'to the surface' of awareness.
Der Taucher musste langsam wieder auftauchen.
The diver had to surface slowly.
Because 'auftauchen' describes a change of place or state, the perfect tense is always formed with the auxiliary verb 'sein'.
Gestern ist eine neue Frage in unserem Projekt aufgetaucht.
Yesterday a new question arose in our project.
In the abstract meaning, 'auftauchen' is often combined with problems, questions, doubts, or ideas. The subject is then usually something abstract.
Wenn neue Zweifel auftauchen, sollten wir darüber sprechen.
If new doubts arise, we should talk about them.
to find
'sich finden' and 'auftauchen' can both mean that something is suddenly there or shows itself. 'sich finden' often sounds calmer and means that something becomes available or an opportunity arises, sometimes without active searching. 'auftauchen' emphasizes more strongly that something appears suddenly or unexpectedly. This can be a person, an object, a problem, or a question. When something simply becomes possible, 'sich finden' fits well. When something appears unexpectedly in a situation, 'auftauchen' sounds more natural.

Vor der Reise taucht plötzlich ein Problem mit den Tickets auf.
Before the trip, a problem with the tickets suddenly comes up.
Für den Ausflug findet sich am Wochenende sicher noch eine Lösung.
A solution for the outing will surely turn up over the weekend.