Origin of particles at the Big-Bang When we read writings on the Big Bang, in Planck's time (and even for some who try to imagine what was before), one talk about particles and antiparticles, but where do these particles and their properties such as charge, spin come from ? one now know the mechanism for the appearance of mass.
 A: The Big Bang (BB) is the dominant cosmological model at present, and for the beginning times it strongly depends on the theory of General Relativity (GR), and GR  includes Special Relativity  (SR)in its limits to smaller masses and energies.
The time of particle creation is definitely in the realm of special relativity, and in SR masses are the length of the four vector describing the system, $(E,p_x,p_y,p_z)$, WhereE is the energy and p the three dimensional momentum of a particle or a system of particles.
So mass is inherent in the modeling of the early universe, and the four vector algebra is very accurate in describing the creation and annihilation of elementary particles and later in cosmological time composite particles, which in the BB model are assumed to follow the Standard Model of particle physics.
At present the BB model is good in modeling observations including the appearance of mass at early cosmological times.
In answer to your comment:

we are directly told about particles and antiparticles (electrons / positrons, quark / antiquarks ...) after $10 ^{-43}$s, where do they come from?

This is the present BB model

During inflation time, the model talks of inflatons, hypothetical carriers of energy and momentum . As expansion grows the packets of energy disperse and there is cooling when seen thermodynamically as an aggregate of four vectors.
In the standard model of particle physics, a quantum mechanical model linked above, elementary particles exist with their antiparticles . A given amount of energy-momentum , a four vector , with invariant mass larger than  twice the rest mass of a particle, has a quantum mechanical probability to form into a particle-antiparticle pair , because quantum numbers will be conserved, they added up to zero before the appearance of the pair, and they are zero after the appearance.
Energy itself comes from the original energy of the BB, which has cooled enough by $10 ^{-43}$s due to the expansion, so these pairs instead of annihilating immediately, travel long enough before annihilating on another, to be counted as electron-positron, neutrino-antineutrino etc. The original BB energy  is an assumption/axiom of the model.
To really understand the model one should be familiar with quantum mechanics, quantum field theory in addition to GR and SR.
A: The distinction that we see between radiation and matter is an artefact of our viewpoint from the present era of the universe. At the massively high energy densities that were present in the early universe there was a high degree of symmetry between radiation and matter - high energy photons were transforming repeatedly into particle-antiparticle pairs, which were in turn annihilating almost immediately to produce photons again.
The two big open questions about the early universe are (a) where did all the energy come from in the first place (regardless of whether it is radiation or matter) and (b) what happened to all the antimatter ?
