This is a bit "out there" but it has been conjectured that entropy is in fact what defines our arrow of time. It's not that entropy increases with time, but rather that our perception of time aligns with entropy increase.
Notably, the thermodynamic arrow of time ties the two together by definition: the thermodynamic arrow of time is simply defined as flowing in the direction of entropy increase.
It is arguably impossible to test experimentally whether our perception of the arrow of time is due to the thermodynamic arrow of time, thus potentially relegating this topic to fringe science. It is however well established that information processing and entropy are intrinsically linked: information processing necessitates a certain entropy increase to occur. This is "widely accepted as physical law" by mainstream science; see Landauer's principle.
Taking this one step further, while disputed, it has been suggested that consciousness may essentially be a form of information processing. Connecting this and the Landauer principle, one can conclude that someone like us asking questions about entropy will necessarily live in a world where entropy increases with time (by anthropic principle).
Obviously this topic sits firmly in the gray area between natural science and metaphysics/philosophy, so take this with a big grain of salt, but it is certainly an intriguing explanation for why we see entropy as increasing.