Trying to get a job in CDMX

SinceIn 2023, I moved to mMexico cCity forto starting my own business with a couple of stakeholders.

(1) Moving to Mexico City is a one-time event and not a state of being, so using "since" here is inappropriate.
(2) "Mexico City" is the name of a place, so it's a proper noun and should be capitalised.

After 3 years of struggling, our business has still not breakoken even yet.

So I tried to practice my oral and written English for the inupcoming job interview.

Last sSunday, I noticed that the TiktTok Shop was recruiting on LinkediIn, and I applied thefor Business Operation Business Analysist without onea second's hesitateion.

(1) The days of the week are capitalised.
(2) "TikTok" and "LinkedIn" are the correct capitalisations.
(3) You can omit the second "I" as the sentence can "borrow" the first one.
(4) The phrase is "apply for (a role or position)". We do not use "the" in this case.

Unfortunately, I got an email from TiktTok today which illustratesnforms me that they won't move forward with my application.

"Move forward" on its own here might not be very clear. I suggest stating explicitly what they won't move forward with; this makes the sentence feel more complete as well.

I felt a little (bit) upset and allowed myself to hold on desperationely to a sliver of hope for like 5 minutes.

I'm not fully certain what exactly it is that you meant to convey with "hold on desperation" (what are you holding on to?), but I took my best guess.

I believe that there's always a waypath forward waiting for me since I won't give up until I'm gonna die.

"Way" isn't wrong, but I think something like "path forward" is clearer.

Die or work hard, and I choose to work hard.

So, wishI hope I can get onea job as soon as possible.

(1) "Hope" is the word to use here, not "wish".
(2) Using "one" instead of "a" places emphasis on the number, on the fact that there's only one thing, which doesn't feel very necessary or appropriate here.