Restoring a Database Using Full Backup and Transaction Logs in SSMS
To perform a restore to (for example) 11:45 AM on October 21st, you need the last full backup that was taken prior to that time, plus your transaction log backups up to and including Noon (assuming the log backups happen exactly on the hour and half hour) on October 21st.

As you do not have a full backup prior to October 25th, you cannot do a restore to a point in time prior to that. With the backups you currently have, you cannot achieve what you're attempting to do.