I'm inferring from reading O.C. 489:1 that one cannot do this. Here, they are specific about the language one must use to count each night.
One particular area that convinces me that you cannot count backwards is mentioned in the Mishnah Berurah commentary #8. There is a discussion as to whether the phrasing is ba'omer (in the Omer) or la'omer (to the Omer). Regardless, of which version one uses, it is clear that one needs to mention the term "Omer" to specify that the counting began from the day that the Omer offering is brought, which was 16 Nissan.
Indeed, the Torah itself in Devarim 16:9 - Deuteronomy 16:9 Sefaria says
You shall count off seven weeks; start to count the seven weeks when
the sickle is first put to the standing grain.
Rash"i explains the date that counting starts:
i.e. from when the “Omer” has been cut (from the sixteenth of Nisan)
which is the first produce to be harvested (Leviticus 23:10) (cf.
Sifrei Devarim 136:2-3; Menachot 71a).
So, it's clear from these two sources that the counting begins the day that the Omer offering was brought and we count the number of days from that point moving forwards. If, on the first day, we said "Today is the 49th day of the Omer" it would be outright false.