I have always thought the way round the grandfather paradox (and also the Butterfly effect) was that someone could travel into the past provided this journey was already accounted for in history. For example one might go back in time to stop the Covid pandemic only to find it was themselves that was patient zero. In other words they were destined to go back in time and make the event happen. This also explains why time travellers have not come back to tell us of their invention. It's not written into the history of time (yet). Either time travel occurrences haven't yet been recorded or they have become disguised over the centuries as mystical events.

I also wonder if time itself is a linear process or does it move forward in waves, faster and slower, but we can't tell it is happening because we are all moving faster and slower at the same rate. We see the clock ticking at a steady rate because we are moving through time faster and slower at the same rate as the clock. This raises the possibility of time occurring at different rates across the universe but time dilation effects mean we observe it as linear. This also means we might be able to travel backwards and forwards in time by 'hopping' from one wave to the next.