Grammatically, the sentence is fine.
My issue would be 'at last' and the point you are trying to convey. Are you trying to show it took a long time and was hard work. On its own, this phrase is more logical:
They reached the North Pole because they made careful preparations ... or ... prepared carefully
If you want to emphasize the length of time:
They reached the North Pole, at last, because they prepared carefully ... or an alternative could be
They were finally able to reach the North Pole because they prepared carefully.