A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

first school • primary school
first school —(UK) a school for children aged between five
and eight or nine: The village would consent to the school
becoming a first school, rather than a primary.
primary school —a school for the first four to eight years of
education: I started primary school in a class together with
fifteen other children, who were all a bit older than I was.
first time • for the first time
first time —said of the very first occasion of smth. (similar
events could possibly follow later though not necessarily): She put
on her hat and shawl and, realizing it was the first time she
was to leave him at home, she hugged and kissed him.
Note:
The expression is not equivalent in meaning to the phrase
first time round
—(also: first time around) used of the first
instance of some cyclic or repeated event: John didn’t pass the
bar exam the first time round. He passed it on his second try.
for the first time —as the first instance since some past point
in time: Negotiations began in the 
1
950s when it became clear
for the first time that coastal resources needed protection.
first time out of the box • just out of a bandbox
first time out of the box —(coll.) said of one’s first experience
with smth.: This is the first time out of the box with these
cars and nobody has had a lot of time to work with them yet.
just out of a bandbox —said of a person looking extremely
smart and neat: They are all exceedingly neat and cleanly as
if they were just out of a band-box.
Note: 
The expression does not correlate in meaning with the
phrase just off the boat—(coll.) used of smb. newly immigrated
and, perhaps, trusting and naive: I showed the students a short
narrative written from the point of view of a new immigrant,
just off the boat.
See also: out of one’s box / out of the box.