Increasing manpower=increasing freemen
As the title says, manpower is a function of your freemen population (in fact freemen on provinces of your own culture-culture group, the others don't count)
So you need that a lot of slaves become freemen (beware, it will affect your income) but not a lot of freemen become citizens (beware, this will affect your research)
The quickest way, as you wait for cultural conversion, is having (getting) the National Idea of Emancipation (in 10 years 7% of your slaves become freemen) and not Citizenship (or in the same time 7% of freemen will become citizens, so depleting your manpower pool). Keep on spankig the barbarians now and then to get a steady flow of slaves into your markets, as money can be a real issue, almost as important as manpower, in the early game.
Later on you will have the oportunity of enacting a law that gives an aditional 2% flow of slaves to freemen. There can be even a law that gives a drop of 2% in the rate of freemen becoming citizens.
Remember the cultural issue: don't expand too much except in regions of your same culture-culture group, use high charisma governors to speed up conversion, etc.