Interlaken is not on the main line that goes from Bern through the alps (two major tunnels) down to Milano. But it is close to a station on that main line, called Spiez, so all your options involve at first a short ride to Spiez where you change trains. It's no problem, you just walk from one track to the other, in Spiez from track 2 to track 3 which is right opposite.
Many options then require a second switch, after you've gone through the first of the two major tunnels, the Lötschberg, and arrive down in the Rhone valley in a town called Brig, to connect with one of the fast trains coming up the Rhone valley from Geneva, and going through the Simplon tunnel down to Italy.
On June 22, you have a train leaving Interlaken Ost at 06:00, or from the other station in Interlaken, Interlaken West at 06:05, that gets to Spiez at 06:21. If you were to remain sitting on that train in Spiez, you would end up in Berlin, Germany by the middle of the afternoon...
So you switch to the train that comes from Bern, arrives in Spiez on track 3 at 06:34 and leaves Spiez at 06:36.
This train goes no further than Brig, where you arrive at 07:11 on track 3.
You walk to track 6 and wait for the train coming from Geneva, arriving at 07:40 and leaving for Milan at 07:44. That means you have a half hour in Brig, enough to get a snack and coffee. You get into Milano Centrale station at 09:37.
The next option is a train that only requires one switch, in Spiez:
Lvg Interlaken Ost 07:29 (track 8) (or I. West at 07:33), arr. Spiez 07:50 (track 2)
Lvg Spiez (trck 3) 08:05, arr. Milano Centrale 10:37
The next two options, leaving Interlaken Ost at 08:00 and again at 09:04, both require the two switches, Spiez and Brig.
It's all at www.sbb.ch/en
You can certainly buy the tickets the day before (or sooner), just mention that it is for June 22 so the correct travel date will be on the tickets.