Assalualikum!
If you look at the flow verses from verse 70 onward, it becomes quite apparent that these verses are primarily addressing the Prophet Muhammad (sws) in relation to His Dawah to Quraysh of Mecca. The appearance of this creature was an original warning to them in case they dismiss Prophet’s message completely. However, few narrations also talk about appearance of such animal/creature near the day of judgement, and there’s no reason to dismiss happening of any such event before the day of judgement as well. Please see the following verses for more detail:
Do not grieve for them [O Prophet!] nor fret over the schemes they are plotting. They ask: “If you are truthful, when will this promise be fulfilled?” Tell them: “The [Hereafter] you want to hasten, it is very much possible that some of it is right behind you.” [The respite you are enjoying at the moment is for your own benefit.] In reality, your Lord is prone to show mercy to people but most of them are ungrateful. Your Lord definitely knows what their chests hide in themselves and what they reveal. There is no hidden thing in the heavens and the earth which is not written in an open book. (27:70-75)
[They should not be led astray by what these people say because] definitely this Quran is also explaining many things to the Israelites in which they are differing and there is no doubt that it is guidance in entirety and mercy for those who believe. [On the Day of Judgement,] your Lord through His decisive directive will definitely decide between them. He is powerful, very knowledgeable. So, trust God; indeed, you are on absolute truth. (27:76-79)
In reality, you cannot make the dead hear nor make your call reach the deaf when while turning their backs they are running away nor can you guide the blind out of their error. You can only make those listen who want to profess belief in Our revelations. Then only they will be obedient too. (27:80-81)
[At this time O Prophet! you are trying to make them understand, but] when Our word becomes conclusive on them We will bring out for them an animal from the earth who will tell them that people did not believe in Our revelations; [so, now they have come before them in the form of God’s wrath.] [1] They should remember the day when from each ummah We will gather a whole army of people who had denied Our revelations. Then they will be categorized. Finally, when they come together, God will ask them: “Did you deny My revelations even though your knowledge could not embrace them or speak up: ‘what had you been doing?’” So, the word will be fulfilled on them because they had been unjust to their souls; then they will not be able to say anything. (27:82-85)
________________________
[1] Ie., it will make evident these facts by its existence. The word تُكَلِّمُهُمْ occurs to convey this meaning. It occurs here in the same meaning as in verse 35 of Surah al-Rum. This will happen because those who are not prepared to listen to the last messenger of God should then only be borne witness to by animals. However, this never happened because most of the Quraysh professed faith in Muhammad (sws). It is evident from various narratives that a similar situation will be created for people near the end of time, and an animal will be taken out from the earth (دَآبَةُ الاَرْضِ) to stand before them.
أَمْ أَنْزَلْنَا عَلَيْهِمْ سُلْطَانًا فَهُوَ يَتَكَلَّمُ بِمَا كَانُوْا بِهِ يُشْرِكُوْنَ.
Ask them: “Have they ascribed partners to God without any basis or have We also revealed an argument that what they associate with God it is bearing witness to it?” (Al-Rum 30:35)