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I forgot my password again! I changed it a few days ago but already forgot!

What is my phone's password this month?

Hint #1:

My passwords do tend to be fairly long, as mentioned in the comments.

Hint #2:

The number itself may not have been on the moon, but maybe something it shares a trait with.

Okay, so first of all, I checked the image and contrast to see if there was something hidden there. I couldn't find anything. Next, I followed the literal interpratation of the text, that is:

The first man to walk on the moon was Neil Armstrong. I tried looking for any items that he wore that would have a serial number or something like that. According to this site, https://www.fratellowatches.com/speedy-tuesday-speedmaster-professional-105-012-with-serial-number-2400xxxx/, the Speedwatches were the only ones used on the moon.

Neil Armstrong's serial number on his watch (again, according to the site) is 24002981, which I believe is your password.

I believe the answer is

1000

I think that we are supposed to take this literally as

"first of the word moon, which is M (1000 in Roman)"

Perhaps the password is

11 or eleven or some variation of it

because

Apollo 11 was the first manned mission to the moon, and it had the “largest number” of anything that was first to the moon, greater that Luna 2, which was the first successful unmanned spacecraft to land.

There are a lot of ways to find numbers that are "first on the moon", so this question may need some more specificity to rule out answers; right now there doesn't seem to be any criteria beyond "the largest" number an answerer might justify somehow, which is probably too broad.

It's possible the password is

201901030226

We know that

OP uses passwords that are usually pretty long, as we learned in Unlock My Phone! January 2018.

We're looking for the largest "first on the moon" number.


China recently made the first landing ever on the far side of the moon - the robotic
Chang'e 4 mission touched down in the Von Kármán Crater at 10:26am Jan. 3, Beijing time.

This is clearly a "first" on the moon, both for China (first moon landing at all) and for humanity (first landing on the dark side of the moon).


If we take the date and time, in GMT, of this moon landing, we get 201901030226. Seconds were not given, so this is the most specific timedate stamp we can get.


Since this is the most recent moon landing, if we were to consider any other "first" - by nation, by mission type, whatever - and take their corresponding YYYYMMDDHMM number, this one would be the largest.

Perhaps the password is

1959

Explanation:

Luna 2 was the first spacecraft to make contact with the moon.
According to Wikipedia, Luna 2 was engraved with "1959 январь" and "СОЮЗ СОВЕТСКИХ СОЦИАЛИСТИЧЕСКИХ РЕСПУБЛИК"1, making "1959" the first number on the moon.
Furthermore, phone passcodes are typically 4 digits long, so using a year as a passcode makes sense.

I think it's:

23.9 billion

Explanation:

According to Wikipedia:
In January 1969, NASA prepared an itemized estimate of the run-out cost of the Apollo program. The total came to $23.9 billion