if we zoom into it, mass won't become zero, suppose we have a ball. inside it are two balls of same mass each, and again inside it are two balls each... it continues... but masses can't be zero. it will halve for ever. Higgs boson is another 'blunder particle' according to me. They are saying that 'higgs' is another virtual particle like graviton... These things are violating conservation of mass and energy. Also another thing is photon. It is a virtual-real particle too. If it doesn't have mass, it won't have energy.
And then the big bang... It is true that Big Bang exists. Your question is, from where does this world come? eerie question... But the only answer is God... this is the sign that god exists.
Another thing is that everything is matter. No energy can exist without matter. And according to me, mass is like a 'container of energy'. Also, we can hypothesize that at its particle form, at a very high temperature, even the gravitational ability will go. At that time the pressure built up will have an energy of more than eV/m^2. At that moment, this force pushes all those particles at near the speed of light (appox.299792457.999999999999999m/s). and will have very large mass and collide with each other and will form atoms and molecules. It will expand at the speed of light and will slow down slowly finally colliding with the gravitational bosons and thus, time and relativity is established again. And finally they form large masses. That's how our universe is born. Then again everything will also go back to the big bang state. This is called the big crunch. again, because of this effect, a cycle forms.