In ancient rome/ ancient greek, it would be quite easy to bootstrap some scientific projects. That period already saw major mathematical breakthroughs and produced some significant scientific knowledge. Archimedes principle for example (250 BC). Architecture was well-developed.
As long as you made each step small enough, what you are doing wouldn't be magic. Of course if you presented microphones and loudspeakers and a working radio first, they might think you are a god or evil wizard, so choose wisely and make sure not to introduce too advanced things.
If you went to the dark ages, then you’d be in for a rough time, no matter how small your advancements are. its called the dark ages for a reason.
I don't have enough understanding of Asian culture to determine whether or not it would be a good idea to go to ancient China. They had advanced knowledge of black powder and rocketry, so it seems they were at least somewhat open to scientific progress.
Some things I'd consider safe:
Advance their knowledge of maths. Use Archimedes principle as guideline, and introduce Newtonian physics. Advance their knowledge of architecture using some new mathematical techniques. Slowly intruduce algebra and differential calculus. Advance their knowledge of materials in small steps, guide them to the invention of steel.
Once they have progressed enough, let them recreate the experiments of Ampere and Watt to have them discover electricity. This will likely be decades after you first arrived. I am not sure if their society would be ready for radio waves by the time you die. But thats a bit up to you. If you invented the letter press shortly after your arrival, they might have used it to further education and might have a young generation that is very open to more advancements. In this regard, the letter press might be your best ally to bring the society as w whole further, because it allows you to spread news and knowledge very easily.
This all depends on you being able to convince the ruling elite to trust you, gaining access to funds, protection and being able to spread your knowledge to other scientists of the same period, and so to give them ideas to pursue so that you don't need to come up with everything yourself.
In that spirit, your first few inventions should probably something that is useful to a ruler so that he wants it and more importantly, wants you to work for him. The more he trusts you, the more tangential projects you can realize.