Was curious as there seems to be a lot of deniers in this day and age, but I feel like if the Soviet union never outright denied the American’s success then it was most likely legitimate.
While more can be said, /u/Dicranurus mentions the Soviet Union's contemporary response to the landings here.
In short, no, they were not denied; they pretended for a time that the "race" didn't exist in the first place.
Your reference to "in this day and age" suggests you are perhaps more interested in what Russians think of the moon landing more recently, which results in a rather different answer but is also past the scope of AskHistorians (we have a 20 year window). You might try asking in /r/Ask_Politics.