الحقونى تانى

[expert]

MR BADAWY
really, i admire your keen and very detailed observation
that expresses your fascination by english language

let's have a brief preview about a / an with ordinal numbers like first , second , third , fourth ...etc

a/an and the are acceptable
examples
the first floor / a second chance
BUT " the " is more familiar due to the very few repetitions that occurs with ordinal numbers

HOWEVER , IN THIS VERY SPECIFIC SENTENCE

After a university education, a first job he did was to work in the theatre as an
actor

GRAMMATICALLY
A FIRST JOB HERE IS IMPOSSIBLE

due to one simple reason ( there is an omitted relative pronoun " that / which " after the word " job" ) so the COMPLETE sentence is

After a university education, the first job that he did was to work in the theatre as an
actor

i hope you are convinced now although i know it is very hard to persuade a man like you

best of luck my friend