Maybe you need to take a step back from a human time traveling and look at a subatomic particle or something simpler?
A sub atomic particle has various properties to manifest it in the physical universe. Its location, its temperature, its electrical properties, its mass etc. Its time could also be a said property. We know how to change the property of many things. Want to change the temperature? Add or remove energy. Want to change the location? Move it. Want to change its time .... mmm. Well this is a property we don't know how to manipulate as of yet. But if you could set its date 100 years before, it should manifest itself in the universe 100 years earlier.
If I look at something 100 light years away, the light hasn't updated its properties and I see the thing as it was 100 years ago. Not as it is now. So using photons I can see back in time using proximity to moderate the property. And I can also slow a subatomic clock by flying it around the world. I'm getting closer. That really is time travel. So energy is the thing I manipulate to change temperature, movement is the thing I can use to change time.
So I will disagree that we can't time travel using a machine. I only need to get in something very fast for a long time and I can go into the future. Thank you relativity.
So now I can see the past, and go into the future. The problem is I can't see the future or go back to the past. The kind of useful ones that allow me to see something before it happens or go back and do something differently.
Now I could see the future, but that would require me to be a long way away and start accelerating to the thing I want to see. So if I'm 100 light years away from earth and I can see WW1 is about to end, I could accelerate towards the earth and find out who wins before anyone else at my starting location knew about it. Because to us the present earth is 1918. But I'd have to get back faster than the light to make any use of this info such as putting £100 on the British to beat the Nazis.
The problem comes that I could only see as far as 2018 because by that point I'm here. I can't go any closer as I have arrived. I'm at the datum point. Figure how to get me through that and we'll go pick some lottery numbers together.
And I can go into the future by travelling very fast like my subatomic clock, but I can't go slower than not moving to get me into the past. Again I have the datum of not being able to go slower than being stationary. At which point I just tick along with entropy (time) like everyone else.
But something I wonder ... if the solar system is moving and the galaxy is moving and the earth is moving etc, I'm always moving. Is that what is making time happen? If I could just get myself to a place in space where no gravity effected me at all and just be still, would time also stand still for me? Would my watch stop if I could get outside of the universe? I'd again theorise it probably should, because sure time is a property of this universe. Outside of the universe there are no physics ergo no time. Probably why God is immortal

I also wonder that if I froze something down to absolute zero, have I in effect slowed its time down to zero. Its electrons stopped, there is no movement, it doesn't change or age in any way. And If I heat things up, reaction happen faster as though I'm pushing them into the future.
So from dimensional analysis everything can be boiled down into units of Mass, Length, Time and Temperature. Or gravity, distance, time and heat, if you like. So I would theorise that Time is a function of Mass, Length and Temperature and by changing any of these things, I could in fact time travel, assuming I survived the freezing, light speed or gravity well. I'd just need one hell of a clever machine to do it.