Chess is still no-hard, so "proving this" will be near impossible.
The closest we have is statistics. I remember watching a "bot battle." A chess tournament for bots only, algorithms playing eachother. Nearly 70% of these games ended in draw.
TCEC is forced to choose very imbalanced openings to make sure there are some non-drawn games. From starting position it'd be 100 draws out of 100 (also all very similar o each other)
