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Which are correct:

1) With the resources they had, it was possible for them to finish the project. I don't know if they did or not.
2) With the resources they had, it would possible for them to finish the project. I don't know if they did or not.
3) With the resources they had, it would have been possible for them to finish the project. I don't know if they did or not.

Gratefully,
Navi

All are grammatically possible except

*With the resources they had, it would possible for them to finish the project.

--> would have been possible...

As regards the sense connections between the sentences, that, as you are well aware, is a semantic issue!

However, I will simply point out that, if you say that something 'was possible' at a certain point in the past, unless context clearly indicates otherwise, it will be assumed that the action/event actually occurred.