All of the routes to Garmisch go through Pasing, but the S1 itself does not.
If you take the S-8 around the east end of town and come in through Munich Ostbahnhof, you'll eventually go to Pasing, and you can catch the train there, but that route takes longer than taking the S1 to the Hbf and catching the train to Garmisch from there. Also, the Pasing station is outside, with only a covering over the platforms - sheltered from the rain but not the cold. Most of the change at the Hbf will be indoors.
By the way, the sign at the airport shows the S1 going to Ostbahnhof and the S8 going to Geltendorf (or another station west of town depending on time of day). Those are the final destinations. The S1 comes into Munich at Laim, goes through the Hbf and ends at Ostbahnhof. The S8 comes into Munich at Ost, goes through the Hbf, Laim, and Pasing, then on.
I was looking at the schedule for this coming Sunday (you didn't give a date). It looks like the schedule changes in a week for weekends, due, I think, to the construction of the new tunnel under Munich.
On weekends, most S-Bahn go non-stop from Ost to the Hbf (no stops under Munich, like at Marienplatz). S8 goes non-stop from Ost all the way to Pasing and gets to Pasing 9 minutes earlier than it does this Sunday. You'll have 13 min to change in Pasing from the S8 to the train to Garmisch. The S1 still comes all the way in to the Hbf from the airport, so you can change at the Hbf.