I thought that the previous alphabet was Cyrillic
No - it couldn't have been. The Cyrillic script has only been developed after X century (and made popular even later, something like XII century). Before Cyrillian script was developed, Cyril and Methodius developed Glagolitic script - which was based on Greek script (although some of the characters are taken from Oriental scripts: Hebrew, Samaritan and Coptic)
Interesting link: ancientscripts.com/glagolitic.html
Texts in Glagolitic are apparently the oldest written Slavic texts.
Glagolitic probably wouldn't have even been introduced on the territory of Poland (due to being formally developed only in IX century) as Poland took Christianity from Rome (with the Latin script) in X century and the oldest scripts found are Latin.
I couldn't find much about scripts prior to Glagolitic and pre-Latin - were we illiterate back then?
Or, rather than that - based on the fact that Poland was on the "Amber Route" - we were likely to use combination of Latin and Greek characters (as most of the amber traffic came from those directions)?