not a minute too soon vs soon

not a minute too soon

• at the last possible moment; just in time 

• after an undesirable delay; undesirably late 

soon

• Within a short time; quickly. 

• Readily; willingly; used with would, or some other word expressing will. 

• Early. 

• Short in length of time from the present. 

• Used as an alternative to express 'to be going to' in the form 'to be soon to' 

• early