I say that you need to maintain the gradient while you fly, but there is more than one way of doing this. Staying at or above the FPM required for your ground speed is one way, but it is very conservative.
The climb gradient can be thought of as a physical floor that starts at 35' at the end of the runway and extends out along the take-off path at the nominated gradient. The only real way to know that you are meeting the climb gradient is to know how many feet per NM you need to gain from the end of the runway.
If you get airborne 2/3 the way down the runway then you are well above the gradient right from the start. Your initial climb is probably quite steep until you get to your acceleration height and so you're even further above the gradient. You can then afford to have a climb rate in fpm that is lower than the fpm/gs table suggests while you accelerate. Once you have cleaned up you are probably climbing quite steeply again.
You have a few options then.
1. Maintain the fpm from the fpm/vs table. This is easy, doesn't require any planning, and ensures you stay above the gradient required. But some aircraft automation systems don't lend themselves to this during the acceleration phase.
2. Check your company climb gradient tables and trust that any periods below the fpm required are more than made up for by the periods above. This is also easy but doesn't give you any guarantees. If you got below the gradient you wouldn't know it.
3. Know how many feet per mile the gradient actually is and monitor this with reference to a known point such as the DME. To do this accurately you also need to know and allow for the distance from the DME to the runway threshold. This requires some planning but is the most accurate and the most flexible as it allows you to reduce below the fpm/gs table while you accelerate while also ensuring you meet the gradient requirements.
I should add that checking the climb tables should be in all three of those options as you need to know whether the gradient is achievable before you depart.
I don't have any references to back this up other than the ICAO definitions for climb gradients for SIDs but the captain needs to ensure the aircraft is performing adequately and, as far as I can tell, those are his/her options for doing so.
Edit: Option 3 loses accuracy once you turn off the runway track.