Why say circle [sIrkl], if we say cat [kæ:t]?
The thing here is about saying the US Great Seal Annuit coeptis according to classic Latin and knowing what and why, not only repeating memorized pronunciation.
Ancient Latin had a sound that modern English hardly has, written as [ts] in many phonetic scripts. We may try to produce it, saying [s] and closing on the hard palate as for [t].
Russian and Polish have the sound in the word ценT or cent, respectively. German has the sound in the numeral zehn, ten.
The Latin centesimus meant a hundredth, and cententionalis was a small coin, all the words here to belong with a decimal idea.
It was the Amber Road to bring the Latin influence. We can compare kwota [kvota] in Polish, квота [kvota] in Russian, and Quote [kvote] in German. French phonology generally would discard [v] within syllables, and has shaped quota as [ko:ta:].
Ancient trade communication was mostly spoken. Italians, more familiar with written Latin, have developed [kwota], let us yet mind that Italian is not “a modern Latin”, however it has [ts] in cena, and [k] in costo.
Assimilation of Latin patterns into English was mostly via written resources as well, English further to have been influenced by French, after the Norman conquest. The French also did not like the speech sound [ts].
In Latin, the letter c stood for the speech sound [ts] — or [c], in phonetic scripts for Slavic languages — before front vowels. Back vowels and all non-vowels brought about the speech sound [k].
We can be back with circles and cats. Modern English words that derive from Latin sound the letter c as [s] before front vowels, and as [k], before back vowels and all non-vowels.
Latin also had digraphs. We can see one in the word cœptis. In speech, the digraph made the sound [e], therefore the c before it resulted in [ts].
Square Roman capitals were a style for ceremonious and official presentations of text. The Great Seal motto would look as here, in the style.
E PLVRIBVS VNVM
NOVVS ORDO SECLORVM
Latin had a specialty about the letter shapes and sounds u and v. For example, we can see the letter u in the word language. The Latin word was lingua, and the way to say it was [lIηgva], as a low vowel followed. The nominative decided for all declension. We may compare cuius [kuIus].
More, there was always the letter shape u to follow every q, together to be pronounced as [kv].
Perseus search: Latin words containing q
Handwritten, the motto would look as
E pluribus unum
Novus ordo seclorum.
There is no context to require sounding u as [v], here.
Here we go,
[a: n n u I t] [ts ε: p t I s].
We may mind that ancients pronounced double non-vowels separately, as in an | nuit.
Feel welcome to read about the Seal.