IME, as someone who leveled up from jr to eventually sr in the same org over a 10yr period, the best advice I can give is be confident in your skills and be willing to take calculated risks.

Teams are always chasing deadlines and resolving unforeseen issues as they arise. The go-getter willing to volunteer to fix a problem that isn't already on their plate gets noticed.

You won't be assigned 'save the day' type work outright as a jr, but the team will find itself in a tight spot, and you need to volunteer to go above and beyond to help fix XYZ even though it's outside your domain.

If you succeed, you have everything to gain. Fail? You're the jr, at least you gave it the old college try while chipping away at your key tasks.