As explained in Do Jews Kneel in Prayer? One is allowed to kneel as long as one puts an interruption such as a towel or a rug on the floor. Please note that we normally do not prostrate ourselves except on Rosh Hashannah and Yom Kippur.
Shulchan Aruch Harav says that the basic halacha is for nefilas apaim (tachanun) after shmoneh esrai, but that we just put our heads on our hands instead of a full prostration.
However, the Code of Jewish Law states that if you put an intervening
substance between your knees and the stone floor, then it is permitted
to kneel.2 Therefore, on Yom Kippur, when we do kneel and bow down
with our faces to the floor, people bring towels to kneel on, since
many synagogues (especially in Israel) have stone or tile floors.
When it comes to daily prayers, however, we are concerned about
transgressing this prohibition and therefore do not kneel in prayer.
Shulchan Aruch Harav 131:1
In addition, any person is forbidden to prostrate himself on a
stone11 floor,4 even when he does not spread out
his hands and feet entirely. This was ordained [as a safeguard] lest
one prostrate oneself with his hands and feet spread out, which
contravenes a Scriptural prohibition12 for which one is
liable for lashes, as it is written,13 “Do not place a
stone floor14 in your land to prostrate yourself upon it.”
[Prostrating oneself on a stone floor] is permitted only in the [Beis
11. The Scriptural prohibition applies only to a stone floor.
It does not apply to a wooden floor, nor to a floor (even of stone)
that is covered with an intervening substance such as linoleum. (See
Rambam, Hilchos Avodas Kochavim 6:7; Rama, Yoreh Deah 131:8.)
Therefore, while saying Aleinu in the course of the Mussaf services of
Rosh HaShanah and Yom Kippur, when it is customary to kneel and to
prostrate oneself until one’s forehead touches the floor, one should
first spread a handkerchief or the like on the floor if it is made of
stone. (See sec. 621:12 in the volume on Rosh HaShanah and Yom Kippur
in the present Bilingual Edition; Sefer HaMinhagim: The Book of
Chabad-Lubavitch Customs, p. 120.)