I'll presume you mean Precocious Spellcaster because "precious spellcaster" got no results. Caster level and Spell level are different concepts in the game. It's kind of regrettable that they use "level" to describe so many things because it prompts a lot of conflation. For the sake of clarity, I will refer to spell level as "spell tier" to help with differentiation.
Ray of Frost is a "tier 0" spell. For comparison, Frostbite and Shocking Grasp are examples of tier 1 spells. Rime metamagic relies on the base tier of the spell to determine the number of rounds it lasts. So a Rimed Frostbite spell will cause entangle for 1 round whereas a spell like Frost Fall, a tier 2 spell, entangles for 2 rounds. Ray of Frost entangles for 0 rounds; hence, rime is ineffective for a cantrip.
Caster Level, on the other hand, just refers to how well a spell scales. For instance, Frost Fall's range and duration increase with caster level, Frostbite's number of uses and damage increase with caster level, and Ray of Frost's range increases with caster level. Precocious Spellcaster lets you count your caster level higher for one tier 0 spell and one tier 1 spell so, as a lvl 1 Sorcerer, if you picked Ray of Frost and Frostbite, you'd calculate the range of your ray, as well as the damage and number of touches for Frostbite, as if you were a lvl 2 Sorcerer. But none of this affects the tier of spell being uses; Ray of Frost is still a tier 0 spell even if cast by a lvl 20 Sorcerer, though its range will be 75 feet (compared to 25 feet for a lvl 1 sorc).
