It is admittedly not easy for me to see what makes you think that adding um would be a good idea here. Once you translate your version back into English you will find that it makes little sense: *Not so easy, in order to squeeze a whole epoch into a few minutes.
What might bother you about the original sentence is its structure. First, you should note that the sentence contains an omission (I'll add it here in squared brackets and will get back to this point later):
a. [Es ist] gar nicht so einfach, eine ganze Epoche in einige Minuten zu quetschen.
This is a simple case of extraposition. Compare:
b. Eine ganze Epoche in einige Minuten zu quetschen(,) ist gar nicht so einfach.
In (b) (the "basic version" of the sentence), the subject consists of an infinitival clause (eine ganze Epoche in einige Minuten zu quetschen). In (a) (the "extraposed version"), the position of the subject is instead filled by (non-phoric) es and the infinitival (subject) clause is moved to the right of the matrix clause. There is no need to add a connector. The phenomenon is very frequent, in German as well as in English. Compare: To squeeze a whole epoch into a few minutes is not so easy. <> It is not so easy to squeeze a whole epoch into a few minutes. / To call her a nationalist would be an understatement. <> It would be an understatement to call her a nationalist.
The omission of es ist is a permissible ellipsis. Ellipses of pronouns occur frequently in the pre-field of V2 sentences and in that case are a feature of colloquial (in particular: spoken) language. For instance: Findest du die Schuhe meiner Schwester schön? - Ja. Gefallen mir! [Instead of: Sie gefallen mir!] / Konnte nicht anrufen, lag noch im Bett. [Instead of: Ich konnte nicht anrufen, ich lag noch im Bett.]. They also occur in connection with the non-phoric ("impersonal") es (Schneit schon wieder.). Analogously, such ellipses occur in copular clauses, where the copula is sometimes omitted along with the pronoun: Ist wirklich schade, dass ihm meine Schuhe nicht gefallen. Or: Wirklich schade, dass ihm meine Schuhe nicht gefallen. [Instead of: Es ist wirklich schade ...]