No I don't believe in coincidences. The synchronicity I experience often was coined by Carl Jung, and is literally is defined as meaningful coincidences. Anyway can experience it, they just have to do that simple amygdala tickling technique.
I was praying to God today as I had worry on my mind about something someone told me, and as I drove home, just before getting home, the car in front of me licence place had the number 777 in it (all together, no gaps) and all within a 20 minute drive. Unfortunately I couldn't take a picture as I was the only one driving, nor would I share someone else's licence place here.
But I've collected many proofs here, even God affecting computers themselves, such as my 777 credit score, or 777 amazon OTP. And all the many "coincidences" I keep collected each day. I don't seek them out, I just happen to be at the right place at the right time.
I think we have the illusion of free will. We still have choices, but those choices don't effect fate. It's hard to kick against the prick. You're being pricked in one direction whether you like it or not. But the choices we make are moral ones. When you rebel and do evil things, filled with envy and hatred, you're just kicking against the prick, your life will feel harder, because you're kicking against fate. But when you have faith, understand life is not fair, succumb to a higher power, count your blessings, and draw near to God, you will find peace, even in bad times, because knowing and trusting that God is in control is a joyous thing indeed.
(Job 4:17-19) "Shall mortal man be more just than God? shall a man be more pure than his maker? {18} Behold, he put no trust in his servants; and his angels he charged with folly: {19} How much less in them that dwell in houses of clay, whose foundation is in the dust, which are crushed before the moth?"
As for your information about time. There's a very interesting antichrist prophecy about this.
First lets remember what God does:
(Daniel 2:20-21) "Daniel answered and said, Blessed be the name of God for ever and ever: for wisdom and might are his: {21} And he changeth the times and the seasons: he removeth kings, and setteth up kings: he giveth wisdom unto the wise, and knowledge to them that know understanding:"
God changes times and seasons. Though I do not fully comprehend it, from what I've experienced with synchronicity, God is so powerful, he can change everything, everyone, including my own will, so I see or experience something at the right place right time (like seeing that licence plate with 777 today).
Now lets look at the antichrist prophecy:
(Daniel 7:25) "And he shall speak great words against the most High, and shall wear out the saints of the most High, and think to change times and laws: and they shall be given into his hand until a time and times and the dividing of time."
Every word in this Bible has meaning, there are 0 mistakes. So when it says "and think to change times and laws", it could mean the antichrist tries to change the timeline, not sure if he succeeds because the word "think" is there.
Funnily enough you mention time travel. Because I was watching something on Amazon prime the other day, and a trailer for Man in the High Castle comes on, and says something like "we defeated the Nazi's in another timeline, surely we can do it in our own" or something like that.
From all my experiences, I honestly think we're more like beings of awareness who make moral choices, and God then does whatever he wants for his pleasure as fate. We are literally watching and taking part in a movie called life, fate, which we are not aware we have no control over.