включиться в работу (vlad-and-slav); разогнаться (With its souped-up new engine, I can get up to speed in this thing in a matter of seconds. Bullfinch)

наверстать упущенное (It took me a while to get up to speed after the flu. Val_Ships); ввести в курс (событий, дела; We have to get him up to speed on what's going on lately. Val_Ships)

набирать скорость (Once the glider gets up to speed, the wings come into their own, and the aircraft can take off Гевар)

вывести на требуемый уровень (The new manager is trying to get the company up to speed. ART Vancouver); разобраться (jouris-t); войти в курс дела (jouris-t); подтянуть (We arranged for some home tutoring to get him up to speed with the other children in his class. VLZ_58); входить в курс дела (thenewstack.io Alex_Odeychuk)

ставить в курс (on ... – ... насчёт ... / with ... – по поводу ... Alex_Odeychuk)

быстро освоиться (on ... – с ... чем-л. • Modern C++ Programming Cookbook. – 3rd Edition, 2024 Alex_Odeychuk)

ввести кого-либо в курс (дела, последних событий)

get up to speed