With any product it is not always easy to establish a ‘day of birth’.
For the 6502 it is the WESCON trade show in San Francisco beginning on September 16, 1975.
For the KIM-1 no introduction event is known. The first publications in magazines about the KIM-1 were in the second quarter of 1976, so press releases and first products must have come from MOS Technology in the first quarter.
Design of the KIM monitor (the ROM in the 6530-002) happened at the same time as development of the TIM monitor (the ROM in the 6530-004) in 1975. The ICs became available end of 1975, see the Hardware manual.
The KIM-1 computer development, with 6530-002 and 6530-003 (the ROM with the audio tap routines), most likely was done in the second half of 1975.
The only real date I can pinpoint is the publication date of the User Manual, January 1976. So I date the ‘birth’ of the KIM-1 computer in January 1976.
I have collected some KIM-1’s over the years. The first KIM-1 in 1978 I bought and sold many over the years. Now I have nine original KIM-1s, from first edition to Rev A, B, D, E , 2x F, 2xG.
The KIM-1 replica by Eduardo Casino (still building, I have original 6530-002 and -003 for it), and a Digitus Sweden clone.
And several reproductions with 6532’s as replacements.

Top row : first edition, Rev A, Rev B, Rev D, Rev E
Middle row: Rev F, REV F, Rev G, Rev G, Digitus
Botton row: Rev D Eduardo Casino, KIM-1 Ralph, KIM-1 Dave Williams, KIM-1 Dave Williams (not shown an unbuilt blue Dave Williams KIM-1).
KIM-1 clones! (Briel MicroKIM, Corsham KIM clone, PAL-1, PAL-2).
Vince Briel was the first to design and sell a KIM-1 clone, the Micro-KIM. Essential was the replacement of the 6530 RRIOT with a 6532 RIOT and an external ROM. The idea came from Ruud Baltissen. The PAL-1 and PAL-2 are still available as kit. The design files for the Micro-KIM are on github.

Top row: Briel MicroKIM, Corsham KIM Clone and PAL-2.
Bottom row: PAL-1 , Corsham breadboard