In an ideal world, the child will be able to choose
If someone suddenly decided that a portion of your possessions will be taken away, you probably won't like it, and your child is the same. Even adults have to go through something similar, for example when an email service provider puts a limit on the number of gigabytes of total emails you can have in your inbox: but you get to choose which ones to delete.
At the age of 6, children can sometimes be surprisingly mature, and you may want to discuss the issue with them. For the majority of your lives, you and your son will both be adults and will have to make decisions together, and the transition from dictator-like parenting to collaborative decision-making will have to start sooner or later.
Age 6 is indeed quite young, but it's worth discussing the issue with them, and if they say "no I don't want to throw any toys away", only then do you have to worry about the next steps:
Consider first how severe the need is to "get rid" of the toys
The only reason you have given for getting rid of the toys is:
"We have no space"
Consider all options: furniture or compartments that make extremely efficient use of space, storage options under the bed, better use of vertical space, use of other storage areas at your residence (if available), etc. I also lived in Japan (Kyoto) for years and had extremely limited space, but it's amazing how much people can store in a small amount of space with a little creativity.
If there's absolutely no way to keep the toys in the house:
First, the space issue is most likely not just because of your children's toys, but sometimes we as adults are also guilty of hoarding some things that others would say we really don't need to keep, so if there's enough for the household as a whole to benefit from an external storage option (monthly fees for this are not too bad, but they do add up over time).
Second, as suggested in the other answer, consider lending or giving some of the toys to a friend who has kids at a similar age. Here's a quote from only 16 days ago from a friend who needed to throw out a lawnmower, but that lawnmower had been in the family for over 25 years and he didn't have the strength to part with it:
"Regarding the lawnmower, that's fantastic if you could use it. I still have it as I don't have the strength to throw it away so if you can use it then that's great."
If you do decide to permanently "get rid" of some of their toys:
As Luke's answer said, there's no easy solution here, and it would be best if the child can have some say in which ones to keep. If you can wait just a couple more years, your child will be that much more mature, and can better collaborate with you in the endeavor to do "spring cleaning".
Your future relationship with your child is probably more significant to you than the inconvenience of going a little longer with the toys
I still remember my mom gave away my first soccer jersey from when I was on a team as a child, and that was decades ago when I was not much older than your son. Not only did it create friction in our relationship but perhaps my present-day obsession with not throwing things away (including digital data and emails!) might be due to losing some things that were sentimental to me when I was a kid.