No. There are two types of particles. Particles that go at light speed and particles that don't.
The particles that don't go at light speed don't do this because they have rest mass. The particles that do go at light speed do so because they have no rest mass. They are massless.
Now what makes massless and massful particles different? This is where the Higgs Boson comes in. There is a field called the Higgs field, which is made by the Higgs Boson.
Particles that interact with the Higgs field are massful. Particles that don't are massless. They thus can go at the speed of light.
For example, photons (that make light) do not interact with the Higgs Field. Hence, they go at light speed. Electrons however do interact with the Higgs field. They thus have rest mass. They thus do not go at light speed.
The Large Hadron Collider verified the existence of the Higgs boson. This is what the "god particle" stories were about in the past decade.
While my understanding of quantum physics is better than the average high schooler, it is still very limited (I possess no mathematical understanding of the standard model whatsoever among many things). Hence, you can gauge the probability of the correctness of my answer. Considering this, here's my answer:
We don't know. We lack a lot of experimental data in quantum physics to answer this question.
So the answer is this: ¯\_(ツ)_/¯