The aggregation, arrangement and bonding together of a set of components to form the CMG complex, a protein complex that contains the GINS complex, Cdc45p, and the heterohexameric MCM complex, and that is involved in unwinding DNA during replication. The process begins when additional proteins (e.g. Cdc45 and Sld3) join the loaded, inactive double MCM hexamer at replication origins, and ends when Mcm10 triggers the separation of the Mcm2-7 double hexamers, forming two active CMG complexes. [ http://www.ncbi.nlm.nih.gov/pubmed/22718908 http://www.ncbi.nlm.nih.gov/pubmed/28501329 ]