Did Mitsuki activate his Sage Mode without...

[Ansatsuken]

In the hand of Orochimaru+Kishi anything can happen.

 

[sandman20]

Kabuto did it with ease and so does Naruto himself later on in the series also what does DBZ have to do with anything? Oh yeah I forgot, DBZ is the 1st Shonen ever created and everyone copies it even explosions :kk:

 

[YellowFang]

Well, for the duration he maintained the form... Naruto or Hashirama could also use it instantly...

 

[UnknownJin]

It should be obvious Orochimaru gave him the ability to do so

Dont ever change ur sig man

 

[Char Aznable]

Mitsuki's sage mode is probably a variant of the curse mark senjutsu from Juugo, the snake sage jutsu that was incompatible with Oro's body (but Oro still learned it) and possibly Hashi cells/white Zetsu (since Oro has created full people like the Shins with similar tech).