Will you force them do this?
it's well known that whatever you do with force you got a double negative effect. so forcing is definitely is not an option.
how you incentivize the miners
what if every user of the coin become a miner, but a miner who not trying to generating a new block and get a reward, but to process the transactions? since there will be no mining rewards there will not be miners just to mine for rewards. all they need to stay online, so their device processes the transactions. since there will be a large number of users there will be a lot of device to process transactions. calculating power will be equally dividend between the connected devices. to add economic stimulus, connected devices can get a reward for staying online and processing transactions. it not necessary to be coins. it can be reputation, trust score, or any other thing that demonstrate your contribution to the network.
how will you stop a malicious attacker build/incentivize bigger power and attack your chain?
have no answer to that. that why i asked what kind of self-defence mechanism can be implemented to the system to be immunable to abuse of power and all other type of attacks. may be making the system not attractable for such type of attacks can solve the problem. parallel systems, attack at the main net trigger the backup or something like this (just fantasising)
So you don't know how

Me neither and I don't see how this could be achieved. I mean that I think that it cannot be achieved.
of course, i don't know) this is what discussion on the forum is about, isn't it? talking, sharing ideas, inventing new one.
let's fantasise. what if the initial spread of the coin to be in some kind of reward for some good things person do, not necessary for the network itself. just in general: it can be reputation, trust score or some like this. as the coin slowly be spreading out there can be other options to distribute it: some can be giving for free to the poor one (the one that are poor not because of the laziness and bad habits, but because of the harsh of the society: not be able to work, even they want to and can). some can be sold (but the money without any exceptions goes straight for support of the network development, charity, disable people who can't work and other stuff that helps to make Earth a better place.)
Trying to make Earth a better place is a good idea, but before starting a new attempt, we should learn history to know what happened with the previous ones. It was never a good idea to simply gather all the wealth around and redistribute it equally among people. It has always lead to many disasters, economical one being among them.
golden words. humanity shows us that it tends to making the same mistakes. mostly it probably because of our nature. some say that wars, greed and laziness in our dna and the only way to cure it is to eliminate humanity. maybe it is so. but maybe there is some way (like that quote from Avengers about only one out of three billion of possible scenarios in which they won) to cure it without elimination. maybe we just don’t discover it yet. like with black holes. 50 years ago they were a myth. but today it is scientifically proven fact (warning: not preaching, just sharing a thought)