Is that for a second just before the engine fires up, or for a second afterwards? First could be starter motor pinion, which might improve with a bit of lubrication ,second could also be that but might also be the drive belt as suggested by Kremmen .
The belt initially runs faster than the cold engine or ancillary . It squeals on the pulley until it reaches the same speed. One possible test is to put some talcum powder on the drive belt /pulley area. If the squealing temporarily stops it points towards it being the belt. Its not a cure , you would then still need to adjust the belt.
Not sure how it works. Some say the talc lubricates the belt so it doesnt squeak when it slips, others say it increases the friction so it doesnt slip at all.