Generally speaking, shouldn't GDP roughly increase equivalent to population growth? With all things being equal: shouldn't the GDP roughly increase equivalent to population growth (as a minimum, setting aside GDP increases resulting from technology, education, and all other factors).

Obviously there are a lot of factors that affect GDP.  However, in general, GDP in one way measures the 'productivity' of a certain population.  If that population increases, shouldn't it naturally follow that the overall productivity will increase proportionally (assuming normal population growth, rather than an influx of invalids, etc).  I assume there would be time-delay in the response of the GDP, dependent probably on the nature of the population growth.
Basically the answer is yes

Population growth is a key factor in GDP growth. Population creates both demands for goods and labour supply

Unlike GDP, GDP per Capita, cannot, obviously rely on population growth, and that is (or at least should be) the goal of governments. and unlike population, the "rest of the factors" affect GDP per Capita just the same

A couple of extra points besides the obvious: population growth, by births or by immigration, affect age distribution, which affects both supplies of labour amd demands for goods and services

Because of it, population stagnation may mean decrease in GDP per Capita and long term economic issues