This is the 14507th most frequent German word.
kämen
"Would come" (subjunctive II form of "kommen").
Here, 'kämen' introduces a hypothetical situation, conditional upon actions of others.
Kämen alle rechtzeitig, könnten wir früher anfangen.
If everyone arrived on time, we could start earlier.
In this sentence, 'kämen' is used in its subjunctive II form to express a speculative scenario under certain conditions.
Angenommen, kämen wir an diesem Tag an, könnten wir die Feier mitgestalten.
Assuming we arrived on that day, we could participate in organizing the celebration.
The word 'kämen' is used as the subjunctive II form to express a hypothetical action that is not currently realized.