The Holy Qur'an says:
Lo! (the mountains) As-Safa and Al-Marwah are among the indications of Allah. (...) [2:158]
How do Safa and Marwah indicate Allah's existence?
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The more exact meaning is that they are an indication, symbol or sign of the worship of Allah. As people do worship Allah by performing sa'y and supplications.
As a reason for revelation many scholars quoted in their tafsir the two ahadith from Sahih al-Bukhari, the hadith on the authority of Anas ibn Malik ():
I asked Anas bin Malik about Safa and Marwa. Anas replied, "We used to consider (i.e. going around) them a custom of the Pre-islamic period of Ignorance, so when Islam came, we gave up going around them. Then Allah revealed" "Verily, Safa and Marwa (i.e. two mountains at Mecca) are among the Symbols of Allah. So it is not harmful of those who perform the Hajj of the House (of Allah) or perform the Umra to ambulate (Tawaf) between them." (2.158) (Sahih al-Bukhari)
ibn Kathir also added quoted another narration in his tafsir:
Imam Az-Zuhri reported that 'Urwah said: Later on I ('Urwah) told Abu Bakr bin 'Abdur-Rahman bin Al-Harith bin Hisham (of 'A'ishah's statement) and he said, "I have not heard of such information. However, I heard learned men saying that all the people, except those whom 'A'ishah mentioned, said, "Our Tawaf between these two hills is a practice of Jahiliyyah. " Some others among the Ansar said, 'We were commanded to perform Tawaf of the Ka`bah, but not between As-Safa and Al-Marwah." So Allah revealed:
(Verily, As-Safa and Al-Marwah are of the symbols of Allah.)"
Abu Bakr bin 'Abdur-Rahman then said, "It seems that this verse was revealed concerning the two groups." (Source: qtafsir)
and which addresses the second longer hadith on the authority of 'Aisha () of Sahih al-Bukhari.
So one major reason for explicitly quoting these two "mounts" in Mekkah is the doubt or rejection of the Ansar to consider worship their as lawful, due to the earlier practices of Jahilya (as one each there was a statue or shrine of an idol -Aasaaf on as-Safa and Na'ila on al-Mawra- before they were removed by the Muslims).
Ash-Sha`bi said, "Isaf (an idol) was on As-Safa while Na'ilah (an idol) was on Al-Marwah, and they used to touch (or kiss) them. After Islam came, they were hesitant about performing Tawaf between them. Thereafter, the Ayah (2:158 above) was revealed." (Source qtafsir)
Al-Qurtubi explained the meaning of "signs or symobols or indications of Allah شعائر الله" (shaa'air Allah) in his tafsir- see here in Arabic- as follows:
In the following I will translate from Arabic, these are my own translation take them carefully
من شعائر الله أي من معالمه ومواضع عباداته ، وهي جمع شعيرة . والشعائر : المتعبدات التي أشعرها الله تعالى ، أي جعلها أعلاما للناس ، من الموقف والسعي والنحر . والشعار : العلامة ،
of the symbols of Allah means from the apparent indicators and loctaions of his worship, and it is the plural of the Arabic word sha'irah شعيرة, and a-Shaa'air الشعائر are the ways and kinds of worship which Allah the almighty indicated, which means he made them a cleasr sign for the people, like the standing (wuquf 'Arafah ), the walking between (as-Safa and Mawra: As-Sa'y) and the sacrifice. a-Shia'ar الشعار -same root as a-Sha'iarah- is the sign or mark.
Imam al-Baghawi commented similarly in his tafsir -see here in Arabic- as follows:
وشعائر الله أعلام دينه أصلها من الإشعار وهو الإعلام واحدتها شعيرة وكل ما كان معلما لقربان يتقرب به إلى الله تعالى من صلاة ودعاء وذبيحة فهو شعيرة فالمطاف والموقف والنحر كلها شعائر الله
and the symbols of Allah are the signs of his religion and it comes from the word al-Isha'aar الإشعار which means the announcement or informing and its singular is Sha'irah and each place which was a sign of worship or to a way to get close to Allah by worships such as the prayer, supplication, sacrifice is such a Sha'irah so the place of tawaf and that of standing (refering to 'Arafah) or that of nahr (sacrifice) are among these signs of Allah.