No according to this answer wich states:
The March 2016 Sage Advice Column covers Dispel Magic as well. It
reiterates that Dispel magic cannot end magical effects that are not
the result of a spell, such as a vampire's Charm effect. It also
reiterates the rule about Dispel Magic not working on the results of a
spell with an instantaneous effect. It adds that a readied Dispel
Magic cannot be used in place of a Counterspell, though in some
limited circumstances, it may be almost as good.
Here's the info:
Can you ready dispel magic to stop another spell from taking effect? The easiest way to stop a spell is to cast counterspell on
its caster while it's being cast. If successful, counterspell
interrupts the other spell's casting, and that spell fails to take
effect. Counterspell works against any spell, regardless of a spell's
casting time or duration.
With the Ready action, dispel magic can be cast in response to another
spell being cast, yet dispel magic can't substitute for counterspell .
The main reason is that dispel magic removes a spell that is already
on a target, whether that target is a creature, an object, or some
other phenomenon. Dispel magic can't pre-dispel something. If a spell
isn't already present on a target, dispel magic does nothing to that
target. The best that a readied dispel magic can do is dispel a spell
immediately after it's been cast to prevent it from having any effect
after the action used to cast it. For example, on your turn you could
say something like this: “I ready dispel magic , and if the high
priest casts a spell on anyone, I cast dispel magic on the target if
the spell takes hold.” If the high priest then cast hold person on
your companion who fails the save against it, you could unleash your
readied dispel magic and end hold person.
The thread: Counterspelling a counterspell might help you.