Yes, seconds hand should start to move once the mainspring is able to provide sufficient torque to overcome the friction of the going train and escapement.
That yours doesn’t until shook, would indicate that something isn’t quite right – a wheel out of alignment or a pivot or jewel dry.
How old is it, and when (if ever) was it last serviced (warranty or paid for)?
Answers aside, it sounds like it’s needing looked at, to see what the problem is, and remedied.
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