If the Higgs boson mediates mass interactions, do they exist in nature? Are there Higgs bosons flying around all the time? Or do they only exist for a tiny fraction of a second while they mediate mass?

As I understand it, the bosons are all mediators of interactions. We know that photons, gluons, and the W-/Z- bosons exist. Photons persist for very long durations as they speed through the cosmos. Does the Higgs/mass-mediating boson do this? I'm sort of having trouble getting a grasp on at what point the mass boson would exist and how that would work in practical fact.

Also, it's entirely possible that this is a nonsensical question based on me misunderstanding everything.