What made cooler temperatures suitable for atom formation? I have read in relation to Big Bang theory that after 300,000 years of big Bang temperature was reduced to 4500 Kelvin and this gave rise to Atomic matter.So,my question is why reduction in temperature makes it suitable for atom formation?
The temperature of a gas is a measure of the kinetic energy of the particles. For molecules you can have rotational and vibrational energy, while for single atoms you just have translational energy, or "thermal motion". At a given temperature, the particles don't have exactly the same energy, but a distribution of energies, and hence velocities.

Most (>90%) of the gas in the Universe is hydrogen. The energy needed to knock the electron off (i.e. ionize) a hydrogen atom is 13.6 eV. For a gas of $T \gtrsim 3000\,\mathrm{K}$, the fraction of particles with sufficient energy to ionize hydrogen is so high, that the majority of the atoms are ionized$\dagger$, i.e. split up in protons and electrons. This was the case in the beginning of the history of the Universe. Everytime a proton and electron met and recombined to form a neutral atom, the electron would almost immediately be knocked off again by a high-energy particle (usually an electron, but it could also be a proton or photons, since all particles were in "thermodynamic equilibrium", i.e. shared the same distribution of energies).

As the Universe expanded, the gas cooled. At some point, 380,000 years after Big Bang, the temperature had decreased enough that it was no longer possible to keep the atoms ionized, so over a rather short period of time ($\sim10^4$ years), they all recombined. This epoch is hence called the epoch of recombination.

Until this point, all photons kept scattering on the free electrons. With the electrons "trapped" in atoms, they could now stream freely, and "decouple". They have been traveling freely ever since, but since they travel through an expanding Universe, they become redshifted along the way. Since then, the Universe has expanded by a factor of ~1100, and so have the wavelength of the photons, so that today they have temperature of $3000\,\mathrm{K}/1100\simeq2.7\,\mathrm{K}$. This is what we see as the cosmic microwave background.



$\dagger$In which case they're in principle not "atoms", but a plasma. However, in astronomy it's quite normal to call it atoms anyway.