That is a misunderstanding of how science concludes that the earth is billions of years old. To understand the scientific reasoning involved we need to cover another philosophical principle. That principle is that the laws of physics are constant everywhere and for all time. This principle can only be accepted as a postulate. It cannot be proven. However I will point out that if this principle is NOT true, that would say something about God and His creation. For example, we know how gravity works here on earth. But we have no direct way to verify that gravity works the same way in a star system millions of light years away. But if we assume that the laws of physics are the same throughout creation we can make calculations about the mass of distant objects based only on the movement of objects in orbit around them. Similarly, we know how gravity works today, but if suddenly gravity were to being working very differently starting in 2022, that would be very distressing to those who are currently on the International Space Station, and indeed for everyone who travels by air, and possibly for everyone in the world if that makes the moon fall to earth. So we accept without proof that whatever the laws of physics are, they are constant over time and over space.
The age of the earth is determined by taking physical processes that we can observe and projecting those processes backwards, making many checks to confirm the accuracy of the projection. If those projections are way off, such that they would lead us to think the 6000 year old world is actually a milion times older, that would again suggest a trickster God who has set things up so the laws of physics are not consistent. Really, it is a great blessing that God has given mankind to have created the universe with such simple laws that our limited human minds can actually figure out those laws just from observing the world in which we live. There was a short story written by Isaac Asimov called "Nightfall". (It was his very first hit.) In that story, a world is described in which their planet orbits three separate suns. In this world, the scientists had a much harder time deducing the laws of gravitation because the system of three suns and a planet is so complex that in inverse square law for gravitation is far from obvious. A similar confusion would result if the laws of gravitation were a discontinuous function of distance and mass. God could very easily have created a world in which none of the laws of physics were obvious. But He didn't do that. He created a world in which the laws of physics are accessible to human minds (mostly) and so life is much easier than living in a world where nothing made sense.
So that's how science determines the age of the earth - by projecting known processes backward through time.
I don't know what you mean by "evidence based faith". It seems like an oxymoron. But the evidence you cite displays a further misunderstanding of science. Saying that there is not enough sediment on the seafloor to support a very old earth is just saying "I know what a billions of years old seafloor looks like." Not only don't you know, you don't even know what would be scientifically consistent with a billions of years old seafloor.
This goes back to the misunderstanding of what science says. Science does not say that it knows in any absolute sense how and when God created the world. What science does say is that certain hypotheses of how and when are more consistent with what we have observed so far than other hypotheses. Currently the hypotheses that are the most consistent with observations are that the earth is 4.5 billion years old. Science say no more than that. Science allows for the possibility of a trickster God that would make such a world that it was actually 6000 years old while being more consistent with 4.5 billion years, but as a Christian, I reject the idea of a trickster God.