Hi Fel.T, and welcome to MySwissAlps!
Yes, that would be possible.
Most people go up to the Jungfraujoch from Grindelwald or Wengen, and return via the other route to take in the scenery from both routes.
In your case, I suggest you go to the Jungfraujoch first via Lauterbrunnen, Wengen and Kleine Scheidegg.
On the way down you have two options to get to Grindelwald:
- Train from the Jungfraujoch to Eigergletscher, Eiger Express cable car from Eigergletscher to Grindelwald Terminal, then a train to Grindelwald station
- Train from the Jungfraujoch to Kleine Scheidegg, then a train from Kleine Scheidegg to Grindelwald station.
From Grindelwald station, you can take a 10-minute walk up Dorfstrasse to the valley station of the First gondola, or else take a bus.
You can plan this trip in the SBB timetable. The timetable is here:
https://www.sbb.ch/en
Information on how to use it is here:
https://www.myswissalps.com/travel/public-transport/timetable/
There is more information about the Jungfraujoch and First on these pages:
https://www.myswissalps.com/activity/jungfraujoch/
https://www.myswissalps.com/activity/grindelwald-first/
I recommend you don’t buy any tickets until the day before your trip at the earliest, to ensure that the weather will be suitable for good views. Forecasts are only accurate 24-48 hours in advance.
You can check the weather forecast here:
https://www.jungfrau.ch/en-gb/live/weather/
The webcams will show you what visibility is like:
https://www.jungfrau.ch/en-gb/live/webcams/
Hope you find this useful!
Alpenrose