There are a lot of new guys like you that strugle with pump and that is why I wrote the article - Why and How to avoid pump during gym training.
I have been a coach and an active climbers for 20 years and even I struggle with pump and that is mainly in even gym routes on top rope. I have recently started to climb half the routes two times in the row instead of getting to pump on a 15 m route and that makes my training better. I know that it would be very good for me to boulder but I have problems in my back and I do not think bouldering is so fun.
In my gym, most 7a climber are actually bouldering so I think this phenomenia is quite common.
The answer to your question is that it is very individual and big guys like yourself will suffer more being pumped. You will gradually improve and get stronger and your maximum strength is what (1) first of all makes you be able to do even a 7a route without being pumped. (2) Later you can focus on improving the blood circulation system by climbing as many hours possible on the wall without getting pumped at all. (3) Finally you can optimize your muscles ability to work better when you are pumped...but this is something you should opt after like five years of climbing and before you want to prepare for a comp or a travel.
At your current level, I recommend you strongly to never get pumped and the best way to progress is possibly to continue bouldering as your main focus. I mean, the problem is that it is so fun to climb a route that sometimes it is impossible to let go after just 8 meters. When you boulder I do not consider this as a pump, but more of being tired in your muscles and this is what you want.