John Gill Commentary Numbers 10:13

"And they first took their journey according to the commandment of Jehovah by Moses." — Numbers 10:13 (ASV)

And they first took their journey, according to the
commandment of the Lord
Which was virtually contained in and signified by the taking up of the cloud, see (Numbers 9:18);

by the hand of Moses ;
by his means and ministry, who had informed them, that it was the will of God, that when they saw the cloud taken up to set forward in their journey, and they were obedient thereunto.