An example of the interpretation
Let's start with a quote from qtafsir (a somehow summarized version of tafsir ibn Kathir):
Allah reminds us of the creating of the higher and lower worlds,
(We constructed the heaven. وَالسَّمَآءَ بَنَيْنَـهَا) meaning, "We made it as a high roof, protected from falling,"
(with Hands بِأَيْدٍ), meaning, with strength, according to 'Abdullah bin 'Abbas, Mujahid, Qatadah, Ath-Thawri and several others,
(Verily, We are able to extend the vastness of space thereof. وَإِنَّا لَمُوسِعُونَ) means, "We made it vast and We brought its roof higher without pillars to support it, and thus it is hanging independently."
My own understanding of this verse is that some kind of expansion is included in the verses, but as the translation used in the quote from qtafsir shows the salafi view is that بِأَيْدٍ is equal to with hands, and may create confusion, if there was not a traditional interpretation as the one of ibn 'Abbas we would have here an issue, as strength would be considered as an interpretation which is not allowed for Allah's attributes by salafi scholars. But this is the meaning that would come to mind to any mindful person who understands Arabic!
However a-Shanqiti (a salafi schoalr) in his tafsir here clearly rejects the idea of that being a reference to the attribute of Allah and say:
ليس من آيات الصفات المعروفة بهذا الاسم ، لأن قوله : بأيد ليس جمع يد : وإنما الأيد القوة
It is not a verse quoting Allahs attributes known by this name, because بأيد (with hands -as it was quoted in the translation from qtafsir) is not the plural of يد (hand), but it is الأيد meaning strength. But his opinion about the linguistic issue doesn't seem to have support in other tafsirs, when the origin of الأيد is discussed.
So his interpretation is we have constructed the heaven with strength.
About the science of tafsir and "scientifc proofs, theories, examples" based on the Qur'an
Before going further we must know that the Qur'an was revealed in Arabic and especially the traditional sunni tafsir scholars would reject any interpretation which was made by anybody else than the Prophet () or a sahabi () which is known for his knowledge of tafsir such as ibn 'Abbas, ibn Masu'd etc. and their students. And of course if the Arabic meaning exists somewhere in traditional Arabic literature such as Jahili poems that might also be accepted. This means an interpretation of the meaning of a word, verse or chapter can only be based on an evidenced source.
So when it comes to so called scientific explanations or الإعجاز العلمي في القرآن (Scientific miraculousness of the Holy Quraan), if the given explanation or interpretation exists, then this can only be based on a meaning in the language, an interpretation given by the prophet himself or a kind of inspiration. Else some scholars among the sheikh az-Zindani have interpreted the verse:
We will show them Our signs in the horizons and within themselves until it becomes clear to them that it is the truth. ... (41:53)
as follows: the "them" in this verse refers to the disbelievers and those who rejected Allahs signs in first place as it is them who will discover their truth (see also this fatwa islamqa #217157), so one way people may discover the truth of Islam is by discovering the truth of its message, not because Muslims show or found this to be truth, but because they were confronted with the truth in their own discoveries ...
On the other hand some of these traditional interpretations may fail if we compared them to scientific proofs or explanations (See for example in my answer on Is it possible for the Qu'ran to have mistakes in it? an example of a rather scientifically wrong interpretation). Therefore other scholars say as Muslims we consider the Qur'an as true, while many scientific theories change with the time, so coupling a quranic statement with a theory is a risky matter, as if this theory would one day considered being wrong we would clearly allow the conclusion that the Qur'an is wrong too.
Some interpretations based on tafsir books
In al-Bahr al-Moheet التفسير الكبير المسمى البحر المحيط the author says that لَمُوسِعُونَ refers to the construction of the heaven so it means we are expanding it's construction, he also quotes some other interpretations such as "we have much strength and power", some said "Energy" others said again referring to the heaven or sky we know: provision by rain and water also the connection to verse (2:236) etc. -already quoted by @Kilise- are quoted. Beside the other option of the meaning of سعة which is a vast space between the heaven and earth.
Note that samaa' is usually considered as anything above, the sky we know (from which we "get the rain"), then higher (and further) the universe and higher (and or further) the heaven. One may be able to deduce the meaning in cases from the context.
Imam at-Tabari in his tafsir quoted 6 traditional interpretations of لَمُوسِعُونَ where the meaning with strength بقوة was used and could find an explanation for any other interpretation to make it fit this (general) meaning (again referring to the verses Kilise has quoted).
Note that Allah says in the qur'an:
The creation of the heavens and earth is greater than the creation of mankind, but most of the people do not know. (40:57)
So the creation of the heavens is a much greater and complex creation than any other creation of Allah, and Allah here gives examples of how even if this creation was that difficult, complex and great HE is able to expand and go further, this is a sign for mankind, as they can only witness the result of HIS creation without being able to observe how. Ibn Ashur gave something like this as an introduction to comment on the verse in his tafsir at-tahrir wa-Tanwir adding that الأيد means strength, but it is originated from the hands, but due to the use of this expression it became a synonym of strength and in this verse and in surat saad أَيْدٍ refers to a strength that nobody can excel!
Does the Quran actually refer to the expansion of the universe?
Well from what I do understand this meaning is not excluded, as in this verse the major meaning is to show the ability of Allah, HIS power and strength to create and expand the heaven, which indeed is a greater and more difficult construct or creation than any other of Allahs creations including mankind and earth. But the point is that Allah refers to a creation we are not able to create, we didn't witness, but only are able to observe the result.