"We started studying late."
Translation:Nosotros empezamos a estudiar tarde.
Some verbs need prepositions to connect them to other verbs (in infinitive) or nouns. This page links to some lists which unfortunately you need to memorise. https://www.lawlessspanish.com/grammar/verbs/verbs-with-prepositions/
the a comes from empezar when it is connected to another verb ( not noun ). empezar la clase, but empezar a estudiar
I wanted to use COMENZAR to answer this. Can anyone comment on what is wrong with 'comenzamos con estudiar tarde'?