We demonstrate a significant simplification of the scheme for few-cycle Optical Parametric Chirped Pulse Amplification (OPCPA) which results in the elimination of a picosecond's master oscillator and electronic synchronization loops. A fraction of a broadband seed pulse centered at 760 nm from a 70-MHz Ti:sapphire oscillator was frequency-shifted in a photonic crystal fiber to enable synchronized seeding of a picosecond's Nd:YAG pump laser. The seed radiation at 1064 nm is produced in the soliton regime which makes it inherently more intense and stable in comparison with other methods of frequency conversion. The remaining fraction of the Ti:sapphire output is amplified with a FWHM bandwidth of 250 nm in a single timing-jitter-free OPCPA stage. Our work opens up the exciting possibility to use sub-picosecond's pump pulses from highly efficient Yb-based amplifiers for jitter-less parametric amplification of carrier-envelope phase stabilized pulses from Ti:sapphire oscillators.