A few facts are stated clearly in the source material (chapters 63 and 121). On the night right after the attack on Wall Maria, Frieda Reiss, her parents and her four legitimate siblings secluded themselves inside the secret cave under the chapel in their family estate. There they were reached by Grisha Yaeger, who murdered everybody except Frieda's father Rod and took the Founding Titan's power, later to pass it to his son Eren by having the latter eat him. According to wiki, this happened in year 845, which was the third year of Frieda's reign. The time limit to pass down the power of the Founder is 13 years (chapter 88), so it was too early.
To my knowledge, the only frontal assessment of a reason behind the Reiss family being in the cave is in an intelligence report that Hange Zoë reads in chapter 62, according to which they had gathered there to pray for deliverance from the disaster. The intel itself was collected by Erwin Smith's spies in the Reiss estate, and it was most likely a cover-up story by Rod Reiss, as recollected by the staff working in the mansion. As those events touch several layers of secrecy, it's clear that the account is generally unreliable (in fact, the same story is untrue in attributing the massacre to "bandits"), however there isn't, to my knowledge, any upfront textual challenge to the claim that they were gathered there in prayer. Obviously we could argue that context might imply that they were hiding in response to an unforseen crisis and, possibly, unknown threats.
As for Frieda's mastery of the Founding Titan, she was reported (chapter 63) to alter Historia's memories, but Rod indeed claims that she was too unexperienced to draw its full power. There aren't many textual evidences that can clarify what "power level" a successor of the first King of the Walls (Karl Fritz) would have in a titan-on-titan fight, nor is it clear how much comes from legends about feats of the past (like building the Walls) and how much comes from actual experience of Rod observing his father and brother. There are textual evidences of the Kings of the Walls having limited access to the Founder's powers, and we could argue that Rod's claim is unclear or questionable due to him not having a full understanding of the Founder's power. More details in spoiler.
It is stated by the Tyburs (chapter 99), that no royal could draw the full power of the Founder Titan in self-defense or in defense of his subjects, due to Karl Fritz's Vow. Due to the Kings never disclosing the truth about the World or their motives, Rod somewhat understands (chapter 66) that Karl Fritz's will prevents the Kings from acting against catastrophes that may befall their subjects (which he believes to be the entirety of humanity), but he still believes that Karl Fritz's will is for the Founder to rule over humanity, which is inaccurate. So it isn't clear if he expected Frieda to draw from some of the legendary powers that the Vow would have prevented her to use, or if he had experience from Uri or his father of a purported "intermediate level" of power that she might have access to and that would have allowed her to beat the Attack Titan.
