There is a way to reconcile an eternal universe with a big bang, which at a casual glance seem to be total opposites.
You see, the universe is about 13.7 billion years old, which is 4 x 10^17 seconds old. When the universe was one-tenth as old as it is now, or 1.37 billion years, it was 4 x 10^16 seconds old.
If we define an "event" as any interaction of subatomic particles (ie an electron emitting a photon, or absorbing a photon), then in the era that the universe was between 4 x 10^16 and 4 x 10^17 seconds old (today), there were a certain number of events, which we can call n.
In the era preceding this one, when the universe went from 4 x 10^15 seconds old to 4 x 10^16 seconds old, the number of events, n, was the same, even though the era only lasted one-tenth as long, because everything was on average ten times closer together. On average only one-tenth the time was required for one event to trigger the next event.
And so on. When the universe was between 0.4 and 4 seconds old, exactly the same number of events happened in that tiny universe as happened in our universe between the time it was 1.6 billion years old and today.
When you get to the nanosecond scale, when the universe was between 4.0 x 10^-10 and 4.0 x 10^-9 seconds old, the universe was only the size of a bowling ball. But inside that bowling ball there were still 'n' events happening, because everything was so close together. There might have been creatures living in that bowling-ball sized universe that thought their universe was enormously old and huge in scale, even though to us they live only an eyeblink after the big bang. Of course their life-processes would operate with totally different principles than chemistry because it was so hot and dense.
There might be creatures who will come long after us, when the universe is perhaps 4.0 x 10^27 seconds old, who will consider our universe as it exists today to be the size of one of their bowling balls. Such creatures would consider us to be living very early in the big bang explosion. This situation would be true for all scales.
So if you grasp what I'm saying, there can be both an eternal cosmos where the universe has "always" been here, and always expanding, in logarithmic time, yet one could simultaneously point to a "beginning" of the universe in linear time. It also means that the Big Bang is not an event that happened long ago. We are living in the Big Bang now.