I believe that the official Star Trek dates are wrong both in absolute chronology and in relative chronology.
there are 2 statements in "Where No Man Has Gone Before" about the length of time Kirk knew Mitchell. Kirk says he knew him for 15 years and Dr. Dehner says Kirk & Mitchell became friends at the time Mitchell entered Starfleet academy (the time mitchell got Kirk involved with the little blonde lab technician).
Kirk says he was a plebe at Sarfleet academy 15 years before the episode "Shore Leave". "Where No Man Has Gone Before" probably happens before "Shore Leave" and so 15 years before "Where No Man Has Gone Before" should be earlier than 15 years before "Shore Leave". It is unlikely that Kirk was a lieutenant and an instructor at the academy before his first year as a plebe there. Thus I deduce that Kirk and Mitchell probably became friends years after they first met each other.
Since Kirk is aged 34 (34.000 to 34.999) in "the Deadly Years" he should be aged about 33.0 to 35.999 in other second season episode. Kirk was a lieutenant making his first planetary survey 13 years (13.0 to 13.999) before "A Private Little war" and (thus when aged 19.001 to 22.999) and was a lieutenant when the Farragut fought the Vampire space cloud 11 years (11.000 to 11.999) before Obsession" when aged 21.001 to 24.999).
A reasonable picture of Kirk's career would be that he returned to Starfleet Academy sometime after the Farragut disaster and became an instructor there.
Kirk's youngest possible age for that would seem to be about 21.001. Kirk's youngest possible age when Mitchell is warned about Kirk by upperclassmen would seem to be about 22.001. Kirk would be 22.001 or older when Mitchell gets Kirk involved with the blonde lab technician. Thus Kirk would have to be at least 22.751 when any possible child of the relationship was born.
Star trek chronologists should try to make common fanon chronologically possible if they can.
3 common pieces of fanon are that first seasons episodes happen before second season episodes, that the "little blonde lab technician" was Carol Marcus, and that Star Trek the Wrath of Khan begins on Kirk's 50th birthday.
according to Memory Alpha:
It has been suggested (such as in the Star Trek Chronology, 1st ed., p. 151 & 2nd ed., p. 268) that a "little blonde lab technician" mentioned in "Where No Man Has Gone Before" may, in fact, have been Carol Marcus. As depicted in the episode, Kirk almost married this female, after an initial encounter between them was arranged by Gary Mitchell (unbeknownst to Kirk) while both males were studying at Starfleet Academy together. Of course, this unnamed character also could have been Janet Wallace, Ruth or some other woman never shown on-screen. Although Michael and Denise Okuda (the writers of the Star Trek Chronology) recognize that the reference might actually be to Carol, they also consider that, given the amount of romantic relationships that Kirk had in his lifetime, it is not surprising that Carol was never heard of (at least not directly) before appearing in Star Trek II. (text commentary, Star Trek II: The Wrath of Khan The Director's Edition)
https://memory-alpha.fandom.com/wiki/Carol_Marcus
https://www.reddit.com/r/startrek/comments/4jy8tg/was_carol_marcus_mentioned_in_where_no_man_has/
http://www.trekbbs.com/threads/st-chronology-idea-kirk-command-school-carol-david-marcus.283932/
If Kirk is aged 50.000 15 years (14.000 to 15.999) after "Space seed", "Space Seed" happens when Kirk is 34.001 to 36.000 years old. Thus "Space Seed" can be as little as minus 1.001 years to as much as 0.998 years before "The Deadly Years".
If Doctor David Marcus is 25.0 to 30.0 in Star Trek the Wrath of Khan he was born when Kirk was age 20.000 to 25.000. If Carol Marcus was the blonde lab Technician David must have been born when Kirk as at least 22.751. That gives a possible time span of only 2.249 years for David's birth.
if Kirk's age is moved to 49.000 in Wrath of Khan "Space Seed" can be as little as minus 0.001 years to as much as 1.998 years before "The Deadly Years" giving more time between the 2 episodes, but Kirk's age at David's birth is restricted to 22.751 to 24.000, a possible range of only 1.249 years.
Of course it is possible that Doctor David Marcus was very precocious and was younger than 25 in Star Trek the Wrath of Khan but we should try to have characters have careers as normal as possible if they can fit in.
A less plausible outline of Kirk's career is that he was a Lt. and Academy instructor before making a planetary survey aged 19.001 to 22.999. If Kirk was an academy instructor for 2 full years he would have begun aged 17.001 to 20.999. And any child of a relationship begun in the second year would have been born when Kirk was aged 18.751 to 23.749 and would be aged 25.0 to 30.0 when Kirk was 43.751 to 53.749. So Kirk would have been an ensign on the Republic when Kirk was no more than 17.001 to 20.999. If Kirk graduated at least 1.0 years before that he would have been no more than 16.001 to 19.999 when he graduated and if he was at the academy for about 3.7 to 3.8 years he would have entered aged no more than 12.201 to 16.299.
This doesn't seem to work chronologically, so a third and least likely possibility for Kirk's career is that he was some sort of lieutenant in some unspecified organization (perhaps as a result of heroic deeds at Tarsus IV) and teaching a course at Starfleet Academy before he ever entered Starfleet Academy and maybe for some years after becoming a cadet at the Academy. Thus there would be no problem with David Marcus being the son of the "Blonde Lab Technician" and being old enough in Star Trek the Wrath of Khan.
Thus we see that it is chronologically possible for the "Little Blonde Lab Technician" and Doctor Carol Marcus to be the same person, but there was only a narrow time period when it was chronologically plausible, and that it was quite chronologically possible for David Marcus to have been born years before Gary Mitchell hooked up Kirk with the "Little Blonde lab technician".
