"ça" is the familiar, short version of pronoun cela.
"this" or "that" in front of a noun are adjectives, therefore you have to use an adjective in front of "époque"
demonstrative adjectives are: ce (masc sing), cet (masc sing in front of a word starting with a vowel or non-aspirated H), cette (fem sing), ces (masculine or feminine, plural):
cet ami, cet homme
cette pomme, cette époque
ces enfants, ces femmes, ces hommes
When there is no context, it is better to translate to the prime meanings of the words you are shown.
If Duo were looking for "période", they would have used "period", I think.
- Cette période = this/that period.
With context, "time" can translate to a variety of phrases:
- At that time, we were happy = en ce temps-là / à cette époque, nous étions heureux
- This time, you can jump = cette fois-ci, tu peux sauter