We observe that the universe is 13.8 billion years old, give or take a little. We can say this because we observe and measure the fact that distant galaxies and the CMB are that far away from us, therefore we're seeing that far into the past. But since only light can travel at lightspeed, how did WE get here (wherever "here" is) before the light from those distant galaxies, or from the CMB? This has always puzzled me.
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You should have a look at "inflation" and the expanding universe. – NDewolf Dec 13 '20 at 10:20
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1We were already here, we didn't have to come from somewhere else. – Javier Dec 13 '20 at 17:29
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I suspect that you should read https://physics.stackexchange.com/q/136860/123208 – PM 2Ring Dec 13 '20 at 17:58
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the CMB are that far away from us Incorrect. CMB is everywhere - relictic photons has filled ALL universe, including our location and others. Simply because BigBang energy with a cooling universe was spread as photons, which we have now as CMB. Why didn't you wonder that any explosion shock waves scatters all particles and debris around explosion scene/volume ? Same phenomena here. BigBang is explosion, which dragged energy / photons / mass (now galaxies) with it. – Agnius Vasiliauskas Dec 18 '20 at 15:35
3 Answers
This like this, there was a small balloon, there is no galaxy on the balloon now it have free dense particles moving around. Then the balloon suddenly expands and the particles become diluted. Now that the balloon is big and the particles are diluted the galaxies start to form. On this big balloon two galaxies are formed which are far from each other. Once they are formed, light starts to leave the first galaxy to move toward the second one. The light gets to the second one after many many years because the balloon is big.
So the answer to your question "how did WE get here? " I should say that we were formed here and the other galaxy was formed over there. we were always here.

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Actually, in modern cosmology we calculate the age of the Universe, using Einstein's General Theory of Relativity, by assuming a suitable metric and computing the age of that model Universe. Thus, the age that you compute depends on the metric that you choose. Now, professional cosmologists have done the hard work to arrive at the number $13.787_{0.020}^{0.020}$~Gyr, by using the currently accepted $\lambda$-cold-dark-matter concordance cosmology model. This is an expanding universe - hence the cosmological cosntant $\lambda$ - with luminous (baryonic) matter and dark matter.
As explained here, computing the age of the model Universe depends on various parameters, the most important for this purpose are the three fractional contributions of various forms of energy to the current energy density of the universe, $\Omega_m$ for matter, $\Omega_r$ for radiation, and $\Omega_\lambda$ for the cosmological constant (which causes the expansion of space in the model), and the Hubble parameter $H$ which describes the expansion rate of the universe. The age of the universe is then,
$$ t = \int_0^{z = +\infty} \frac{dz}{H(z)}$$
where $z$ is the cosmological redshift and, where $H(z')$ depends on the cosmological parameters from above for the FLRW metric which is the foundation of the $\lambda$-CDM model.
For some historical context, in the early 1900's, a synthesis of cosmology occurred: Einstein's theory of gravity allowed for rigorous modeling of the universe, observations began to show that the Universe is full of lots of galaxies, and Hubble showed that these galaxies are receding from each other - the traditional interpretation of this is that the universe is expanding. Through the foundational works of Lemaitre, Friedman, and the 100 years of study following by thousands of others, cosmology is more a precision science than ever before. These models are "big bang" models which assume the universe begins from a singularity and expands thereafter. So, this means that the "big bang" occurred at every point all the time, in the very earliest moments of the Universe (on a distance scale smaller than we can even theoretically probe), and the Universe expanded from that initially low entropy, high temperature state to the increasingly high entropy, low temperature state we see today.
So, when we observe a very very very far away galaxy to have a distance greater than $14$ Gyr, we may be puzzled, and indeed this was a problem called the cosmic age problem. Nowadays, most cosmologists believe that this problem is solved, by interpreting data concerning the expansion of the Universe: the Universe's expansion is accelerating, which explains why the relative distance of some objects can appear to be greater than the cosmic horizon (and why the recession velocity can appear to be greater than the speed of light). See here for a better explanation.
I'm not a cosmologist, so I hope I haven't said anything too imprecise. :)

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The galaxies were formed after the inflation which means at the time of formation the distance between the galaxies were already huge.