When a sound is coming towards me and the wind is also towards me, can I hear this sound sooner?
Yes, the wind blowing towards you will help sounds carry further and also faster, but it is a little more complicated than you might think. Imagine if it was the other way around, with you shouting into the wind, then you would have problems, to say the least, in getting your message across to someone upwind of you.
Sound waves, (longitudinal compressions and rarefractions of air) will be bent downwards when travelling with the wind.
Conversely, sound waves travelling against the wind, will undergo a refraction in an upwards direction.
The black arrows on the drawings indicate the direction the sound is heading towards.
Gusty winds will make someone upwind of you even less likely to hear your voice, as it will undergo more distortion than a steady breeze blowing against you.
Images from: Sound Waves and Refraction.
Sound waves, like transverse light waves passing through a prism, undergo a refractive process, tending to move towards the ground when moving with the wind, and away from the ground when they are moving in the opposite direction. Friction with the ground slows the wind down, so the lower layers of air /wind move more slowly.