Can I react to a battlefield's hold ability during the beginning phase even if there are no units at the battlefield?

No, you cannot.

According to Rule 383.4.d, "Hold Effects are Triggered Abilities with a Condition of a Unit being present at a Battlefield during the Beginning phase when a player scores Victory Points from Holding." Furthermore, Rule 383.4.d.2.a specifies that the hold abilities of units are put on the chain only after the units they correspond to are present at a battlefield when a player maintains control and scores the point.

If there are no units at the battlefield, you do not meet the criteria to score a point for "Holding" that location. Because you are not performing the "Hold" action, the triggered ability never meets its condition to be placed on the chain, and consequently, there is no trigger to react to.