Well, given that there is no universal clock and time is defined locally for each observer, including each particle, it would be more strictly accurate to say that "the matter which later formed our solar system has experienced 13 billion years of time" since the Big Bang

or maybe 13 billion years is from the frame of reference of the Cosmic Microwave Background? that would make more sense. I'm going to check again then edit this comment.

(i am not a physicist, not an authoritative source on this)

edit: so it turns out that the age of the universe is given from the frame of reference of the CMB rather than from Earth's frame of reference.:

> Measurements of the cosmic background radiation give the cooling time of the universe since the Big Bang

> Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology.[1][2][3] Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time (the fact that this is possible means that the universe is, by definition, homogeneous). The clocks measuring cosmic time should move along the Hubble flow.

https://en.wikipedia.org/wiki/Cosmic_time