Do you believe that scientific investigation is the only effective method to gain meaningful knowledge about the universe?

This is a wrongly-phrased question, as it falsely implies that the only alternative to “scientific investigation” must be faith or magic or religion or something along those lines. I have a very specific idea of what “scientific investigation” means: any such investigation must adhere to the scientific method, which means a falsifiable hypothesis must be presented, then a repeatable experiment carried out and its results compared to either falsify or support the hypothesis, followed by peer review, etc.

In contrast, consider the advancements made by theoreticians like Pythagoras, Plato, Descartes, Einstein, Schrödinger, Heisenberg and Hawking, who did not actually adhere to this scientific method, but instead devised so-called “thought experiments” to further our knowledge using only introspection on already existing data, rather than taking observations on the physical world.

Therefore, there exist ways to gain meaningful universe without resorting to science. As far as I can tell, these methods instead relied on logic, math and perhaps philosophy.