At low tide, paddling in Gulf Pond will be limited to a narrow channel that meanders through the mud flats. At very low tide you may ground out on shellfish beds in some spots.
At mid to high tides the entire pond is canoeable. There are three bridges crossing the pond and within an inch or so they have the same clearance over the water.
At higher high tides the clearance can be too low to clear in a canoe or kayak and one should approach the bridges with caution if the current is pulling their boat towards the bridges. The bridges at Gulf Beach and Buckingham Avenue can be portaged, but the New Haven Bridge abuts private property on the south side. The current during full flood or ebb is swift although a strong paddler can make it upstream with 50 yards of effort under any of these three bridges.
The Indian River is entered at the railroad bridge at the top of the pond near New Haven Avenue. There is more than a foot of jagged rocky bottom gradient from Gulf Pond up into the river but, the tides back up at this narrow opening, and it can be paddled near high tide.
The best strategy is to arrive at the top of the pond a little before high tide, ride the current in (it is fast, but easy), explore for one to two hours and ride the ebb current back into the pond. At full flood and ebb the current is much too fast to paddle against. The passage can be waded at low tides. It is a bigger problem at mid tides when the water won't be a pleasant wade and the water isn't deep enough to clear some of the large sharp rocks in the passage. Upstream of I95 there is one more bridge with low clearance. At peak normal high tides there may not be enough clearance to go under. It can be bushwack-portaged (I just wait it out when this happens), but watch the traffic when you cross the busy road. Also, upstream of that bridge you may have to do a some wading at mid tide or lower levels.