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The start of the calendar has to be arbitrary, there’s no way around that as it’s not feasible to measure the time since the beginning of the universe with good enough accuracy.
As others commented, the Julian Day is a time measure that is actually used in astronomy, and Unix time is a time stamp standard (not really a calendar, although it could be if we got used to it) that is mostly a way to store time points, not really to consume them before converting to a more readable form.
But as a scientist who is wholly irreligious, I’m not overly bothered by using the Gregorian calendar, even though it has Christian (and a lot of pre-Christian) elements. Its annoyances (different numbers of days in each month, weeks not aligning with years, leap years etc.) are due to the fact that we decided to measure time in these arbitrary units. At least it’s universal in the modern era (often in conjunction with another calendar), and everywhere you go people understand what “August 5, 2024” means (although August might have to be translated to the target language, since the names of the months are not universal).
That’s more than you can say about non-time units of measurement (I’m looking at you, imperial and US customary units!!)
Interestingly, that is not the case. Month names can differ in different languages. I discovered the hard way that Ukrainian has completely different names for months when I had to connect to a Linux machine in Kyiv with Ukrainian locale (I can read Cyrillic, but the abbreviated month names meant nothing to me). The name for August is “serpen” by the way, and it is similar in some other Slavic languages. Also Arabic has its own month names based on Akkadian, August is “ab” but an Arabized version of the word August is also commonly used and understood. Finally, in Mandarin and presumably other Chinese languages, Gregorian months are only referred to by their number, so we are in “bayue” (lit. eight(th) month).