I have a spot picked out for a compost heap but it is currently bricked.
Is there any benefit to waiting till I can clear it or should I start composting right away?
There are a few things that I would consider, but they are not necessarily show stoppers.
If you place the compost bin on the soil then it will be easier for bugs to get into your compost and speed up the composting progress. This can be overcome by purchasing worms from a supplier, but I am sure there are plenty of other things that you can't see that would arrive if they had an easy path upwards.
Sometimes you need to add water to your compost heap if you have an excess of brown and not enough green going in or if it rains heavily water can go through your heap. If you have your bin or pile next to an area that you want to keep clean or where this water can pool it might stink or become unsightly.
How inconvenient is it going to be with bricks in the way if you need to either shovel your compost from the bottom or if you need to turn the pile and bring the stuff from the bottom to the top.
Again, these are not show stoppers, but something to consider.
In my opinion, there is probably no benefit to the compost heap either way.
However, there may be a great benefit to the soil should you relocate your compost heap to a new location as a lot of the goodness from the compost heap will have leached into the soil and that path would now be a great place to plant a tree or any other vegetation.
The bricks might be stained by what you put in the compost and, again, if you were to move the compost it might not be possible to clean the bricks or use them again.
Do you mean is there a benefit for compost being on top of soil vs being on top of bricks or concrete?
If you put the compost pile on soil, you will have earthworms in your compost, which is considered a good thing.
If you put the pile on bricks, I can't see how the worms would get into the compost unless you put them there... or by magic.
That said, people use special bins or compost tumblers all the time, so maybe it doesn't matter either way.
Start composting now and when you feel like moving the bricks, move the pile and move the bricks, then put the pile back. The sooner you start composting, the sooner you can use the compost.