Assalaamu alaykum. It is stated in the Quran (what means): {And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous.} [Quran 2:133] And we know that the universe is still expanding. So is it true that Paradise is also limitless?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

We do not know whether what you mentioned, that the universe is still expanding, is an established scientific fact or not. In any case, the verse mentioned is in Soorah Aal ‘Imraan [Quran 3: 133] and not Soorah Al-Baqarah [Quran 2], as you stated. It comes in the context of underlining the extensive width of Paradise and is not intended to underline that Paradise is exactly as wide as the Earth and the Heavens. Some scholars underlined that the meaning of the verse is to highlight the vastness of Paradise and not to underline that the width of Paradise equals that of the Earth and the Heavens.

Al-Baghawi wrote:

“The width was mentioned as an exaggeration because the length of everything is often greater than the width. So if Paradise is this wide, then how long would it be? Az-Zuhri said, ‘Only its width was described; as for its length, Allah alone knows it.’ This is only a metaphor, not that it is as wide as the Heavens and Earth and no more. It means that it is as wide as what you think the width of the seven heavens and seven earths is, like the verse: {(They will be) abiding therein as long as the heavens and the earth endure.} [Quran 11:107] It means according to your assumption because the heavens and earth will eventually perish and cease to exist ... Anas ibn Maalik, may Allah be pleased with him, was asked about Paradise; whether it is in the heaven or on this earth. He answered, ‘Which heaven or earth could encompass Paradise?’ So he was asked, ‘Where is it then?’ He answered, ‘Above the seven heavens, below the Throne.’”

It should be noted that the Muslim should not concern himself with (asking questions about) matters that do not lead to doing good deeds.

Allah knows best.