Is the universe eternal or temporary? It is most importantly observed to differentiate illusion and truth.
This illusory world is both eternal and temporary.
ध्रुवं कश्चित् सर्वं सकलमपरस्त्वध्रुवमिदं
परो ध्रौव्याऽध्रौव्ये जगति गदति व्यस्तविषये।
समस्तेऽप्येतस्मिन् पुरमथन तैर्विस्मित इव
स्तुवन् जिह्रेमि त्वां न खलु ननु धृष्टा मुखरता॥ ९॥
O, Destroyer Of ( Three ) Cities Shiva, some persons call this Universe eternal ( ever lasting), others call it temporary, and yet others call it both eternal and temporary . Hence, being surprised ( perplexed ) by these contradictory opinions on this subject, I am really becoming immodest in loquaciously praising You .
From Mahimna Strotra
The Absolute GOD is universal, omnipresent and all knowing. Nobody is able to destroy it. And Illusory world that we see which is relative is temporary upto our death or judgement day or end of our time on earth.
Also in Shrimad Bhagwat Geeta Lord said
avyaktanadini bhutani vyaktamadhyani bharat avyaktanidhannyanaiva tatra ka paridevana
This universe is always disappeared in start, appearing in middle and again disappeared in end.
Ashtavakra geetha verse 10.2 :- Look upon friends, lands, wealth, houses, wives, gifts-- and all apparent good fortune-- as a passing show, as a dream lasting three to five days.
verse 18.1 Praise That, which is Bliss itself, which is by nature stillness and light, and which by Its knowing reveals the world as a dream.
Also the story of Narada asking Krishna to show him the power of Maya confirms and reiterates the fact of life being just a dream.
Does a dream have a start? Does it have an end? All we can say is that it is not real. We can dream for ever and hence it is not temporary. We can wake up and end it once and for all hence it is not permanent.