Oops, you're not clear on much of anything. This will make it hard.
Big bang? It didn't start out as matter, but rather as energy. Now, if you want to know where the energy came from, you're out of luck. We haven't figured that part out yet. But don't worry, we're working on it. It may be that we could have already had the answer if we didn't have so many theists thinking there is nothing to look for and hence they missed out on being great scientists. That's just speculation, but I enjoy speculating.
Age of the earth? No, it's not just layers. The layers didn't start for a long time. We were too busy being molten for awhile, then too busy being smashed into by giant pieces of space debris for awhile, and making our moon via another giant collision for awhile, and it simply took more than a day to put the place into good enough shape to start making layers and such.
So we actually date meteorites that have fallen to earth. On the assumption that they were made at about the same time as the rest of the material in the solar system, it makes sense that the oldest rocks were formed at about the same time as earth, but elsewhere. So they didn't get melted over and over by the various forces that kept earth molten for so long. And if we measure said meteorites using various forms of radiometric dating, we keep getting dates of around 4.5 billions years ago, no matter what the oldest meteorites are made of. And we can't come up with any good reasons to think the planet is any younger.
The oldest rocks native to earth are dated at about 3.5 billion years old. Some are in layered formations, some are not. Not all rocks are layered. Specific geologic conditions are required for that to happen. If, as the creationists say, all layered rocks were formed during and shortly after the flood, one has to ask why there are so many rocks that aren't layered. A universal flood of that magnitude should end up with, oh, I don't know, universal layering? Makes sense to me.
Anyway, we can use radiometric dating (and there are a variety of things to date using the basic method. Lots of different isotopes that can be measured and whose decay can be extrapolated backwards. We keep getting similar dates, which we jump to conclusions about and assume mean that the oldest rocks are about that age. But we jump to those conclusions because we can't find any other conclusions to jump to. Forgive us.
There is layering, of course. Whose ages, sadly, match up very nicely with the ages found using radiometric methods. It is very awkward that the dates seem to agree with each other. Because it forces us to use science to explain our results, and that throws theists off something fierce. It would be nicer if we could just discover some nice old folk tales that did the same thing, but so far we haven't found any. All we've got are the freakin' rocks.
Notice that I haven't mentioned carbon dating. Don't consider this a personal affront. It's just that carbon dating only works on stuff that was a) alive and b)no more than 60,000 or so years old. So any claim that recently offed critters were measured using those methods and shown to be millions of years old means that whoever did it didn't know a darn thing about calibrating their instruments, let alone what the heck they were doing. But being misinformed tends to cause similar outcomes all the time.
Anyway, we don't have to depend on carbon dating. What we have are a whole bunch of different clues as to the age of the planet, and they have a bad habit of matching each other. We can look at chemical compostion, geologic layering, plate techtonics, atmospheric gases, the genetics and structure of ancient fossils, which have a real bad habit of being buried in successive layers that match the evolutionary progress of the various creatures. And we have modern genetics, which can predict the sources of the original genes and then look to see if the fossil and geologic and biologic records match, and darn it, they do. Se we are stuck, at least for now, with all this corroborating info that matches nicely.
Decaying doesn't happen at random, by the way. There are constants that, at least so far, have proven to be pretty darned "constant", if you get my drift. We can't think of any reason they would be otherwise. All evidence points to their reliability. If they aren't, we need to get busy right away rewriting our chemistry books.
If decay were random, isotope wise, I assume it would be random everywhere else, because obviously any god worth his salt (until it decayed) would deliberately toss in randomness everywhere. Some rocks would stay real hard and be good for bopping slow antelopes over the head, while others would get soft and mushy and we'd step in them and go ick. Random would suck. I like constants better. But we could take a vote.
And I noticed you forgot to ask about the million year old ice cores we have drilled out of the Greenland ice cap. I assume that was an oversight on your part. Now I know a million years isn't anything close to 4.5 billion, let along over 13 billion years, but it sure puts the kibosh on the silly 6,000 year old earth theory that some folks toss around like facts. Unless some dofus writing the bible left out the verse "In the beginning, god created a million years worth of ice in the Greenland ice cap just to fool the people he loves". Or maybe I just missed that verse.
I could have gone into more detail, but you didn't seem too well prepared for actual information, so I went easy. Thank me later.
But there will be a test on this material Monday morning. Come prepared.