Microgauss magnetic fields are observed in all galaxies at low and high redshifts. The origin of these intense magnetic fields is a challenging question in astrophysics. We showed that the natural plasma fluctuations in the primordial universe, produces random dipole magnetic fields of comoving size $∼ 1$ pc and intensity $∼ 0.1 μ G$ at a redshift z $∼$ 10. The theory predicts an average magnetic field $∼ 0.003 ~ nG$ over a 2 kpc region at z $∼ 10$. We assume this seed field and examine its amplification by a turbulent dynamo in a protogalaxy. Whereas the standard $α-Ω$ dynamo for a typical disk galaxy creates only a 2 e-fold amplification of the field in $∼ 10^9$ years, the turbulent dynamo has a much shorter amplification time. Starting with the average seed magnetic field of $B∼ 0.003 nG$ over $∼ 2$ kpc at z = 10, we find that in $10^9$ years, $B$ is amplified to $∼ 1 nG$. This corresponds to a $∼ 6$ e-fold amplification of the field. In the process of collapsing to form galaxies at $z∼10$, the plasma density rises by a factor of $∼ 200$ and the magnetic fields, by a factor of $∼ 34$. Thus, $0.03 μ G$ fields over 0.34 kpc regions in galaxies are predicted. If the dipole magnetic fields predicted by the Fluctuation-Dissipation-Theorem are not completely random, microgauss fields over regions $\gtrsim 0.34$ kpc are easily obtained. The model is thus a strong candidate for resolving the problem of the origin of magnetic fields in $≤sssim 10^9$ years in high redshift galaxies.