Hi! Don’t worry at all! Applying a few weeks after an application window has opened
will not disadvantage you

In fact, I’d say whether you applied on the first day, or half way through the window, you have an equal chance. No advantage or disadvantage either way.
Both rolling and non-rolling firms typically receive 50% of all applications during the last 2 weeks (before their deadlines close).
As long as you submit a strong application, it doesn’t really matter when you submit it for 99% of firms.
This is even more true given your intention to submit only a few weeks after an application window has opened.
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(Most firms aren’t fully rolling-basis, even if they claim to be. However, there are one or two firms that genuinely recruit on a first-come, first-served basis. But, we’re so early into the application cycle that I wouldn’t worry. If a winter scheme was hypothetically full because you were the last person to apply, you’d be considered for the spring and summer schemes instead.
What therefore matters is submitting a strong application, rather than the timing of when you submit).