Some of the things that hampered TL change here, are not discoveries as such, they are inovations, or practaces.
Things like time and motion studdies, standerdisation, production lines, etc you can work out at any TL you don't have to wait until TL4 to "discover" these. And these type of discoveries will increase efficancies driving TL change forward faster.
And inovations like the paper clip. You could have the paper clip in the iron age, you don't have to wait 1900 years to inovate this product.
Other things you need to generate are wealth and population. Wealth to allow an amount of the population to expand the realms of knowledge (If you are all subsistance farmers you won't have any da Vincis), and population size (so you can have more than one da Vinci).
Another driver for TL advance (apart from war) is information sharing and peer review. If you can foster information sharing far earlier, you can advance TL quicker.
Best regards,
Ewan
Certainly there are many items that could be created at lower TLs, but there are also some things that can't - such as transistors.
However, the issue here is that whether TL7 is achieved after 5000 years or after a mere 500, you are still going to need TL7 (or at least TL6) in order to get into space.
A lot depends on how your TLs are defined, though. According to LBB3, the availability of lasers, hovercraft, spacecraft and (photovoltaic) solar power are the defining descriptors of TL7. If you have them, you are at TL7, if you don't, you're not. If you have some of them but not others, you can argue about whether you've reached TL7.
However, looking at the defining descriptors of TL6 - guided missiles, television, submersibles, and fission, these all seem to me to be essential precursors of spaceflight.. Without the knowledge gained from guided missiles, or the remote operations afforded by television, or the sealed environment functionality derived from submersibles, or the physics/electronics breakthroughs engendered by an understanding of sub-atomic particle interactions, I cannot see how manned spaceflight could possibly be developed.
Late TL6 appears to be an absolute minimum for spaceflight.
Throwing money at the project may reduce the time it takes to achieve the TL, but it won't reduce the TL required.