It is possible to self-initiate into the spiritual side of Freemasonry!
But there's a catch...
You have to be a Freemason first in order to do so!
What I mean is: one of the big things about Freemasonry is about Brotherly Love (the other two being "Relief" and "Truth"), so if you try to become a Freemason whilst missing out on the Brotherhood that comes from being part of a lodge, you're kind of missing the point.
That being said, when you actually get into Freemasonry, you will find that the vast majority isn't actually either spiritual or esoteric, unless you happen to join a lodge which was specifically set-up to be so, such as a Memphis Misraim lodge, or one which follows the teachings of W L Wilmshurst or C W Leadbeater.
Hence, in order to be both a Freemason and into the spiritual side of the Craft, you will of necessity have to take on a lot of personal responsibility to do so, treading a lonely path unless you happen to make contact with like-minded Brethren. For example, there is a lot of inner-work to be done like meditation, self-study, etc. However saying that, the good news is that spiritually minded Brethren are out there: for instance you could try googling the Dormer masonic study circle.
Fraternal best wishes,