

There are core concepts that are likely to be universally understood.
Maths is probably the best and most common example. If we imagine the symbols have been removed and we work under the assumption that we’re manipulating objects we can show that 1 object + 1 object = 2 objects without any language necessary. From there we (aliens and humans) can work together to build a common foundation of understanding.
Don’t get me wrong, this will not be easy and there will be problems we haven’t thought of but there’s a good chance that a spacefaring civilisation will know enough about mathematics to build a new common language.
It’s definitely a contender, I’m not sure it’s “much simpler” though. There is no simple option, it will likely be the most challenging linguistic problem the world has ever faced.
Assuming the periodic table will be the same is a huge leap. @themeatbridge@lemmy.world did a good job of explaining why in another comment. To paraphrase, our periodic table is limited to our perspective of the elements. There could be other even more accurate, and descriptive ways to fully encompass what an element is.
Maths already is a language of sorts, with logic built in. Whereas the periodic table is a technical description of elements.