The pandemic state of COVID-19 caused by the SARS CoV-2 put the world in quarantine, led to hundreds of thousands of deaths and is causing an unprecedented economic crisis. However, COVID-19 is spreading in different rates at different countries. Here, we tested the effect of three classes of predictors, i.e., socioeconomic, climatic and transport, on the rate of daily increase of COVID-19 on its exponential phase. We found that population size and global connections, represented by countries' importance in the global air transportation network, are the main explanations for the early growth rate of COVID-19 in different countries. Climate and socioeconomics had no significant effect in this big picture analysis. Our results indicate that the current claims that the growth rate of COVID-19 may be lower in warmer and humid countries should be taken very carefully, risking to disturb well-established and effective policy of social isolation that may help to avoid higher mortality rates due to the collapse of national health systems.