It is well-known that GNSS precise point positioning (PPP) has been suffering from slow convergences or long initializations of up to tens of minutes. Rapid PPP convergence is essential to some time-critical applications, such as vehicle navigation in the urban valley, earthquake early warning and weather forecasting. Therefore, it is desired that PPP can converge rapidly to ambiguity-resolved solutions (PPP-AR), within an observation period of a few minutes, to a better than 5-cm positioning precision, at least in the horizontal directions. In this study, we propose to shorten PPP convergence time with the aid of advanced multi-frequency data (e.g., E6 and B2a signals) from Galileo and BeiDou-3 satellites. It has been demonstrated that the ionosphere-free wide-lane GPS/BeiDou/Galileo observables, constituted by wide-lane (e.g., L1/L2, B1I/B2I and E1/E5a) and extra-wide-lane (e.g., L2/L5, B2I/B3I and E5a/E5b) observations, can achieve ambiguity-fixed status within several epochs of data. They can then be used as “carrier-range”, instead of pseudorange, to constrain narrow-lane ambiguities and speed up their convergences to high-precision estimates. In this case, PPP-AR can be achieved more rapidly in theory than that when only dual-frequency data are used. However, since the noise of such GPS/BeiDou/Galileo wide-lane carrier-range is more than 100 times larger than the original carrier-phase noise, their contribution to accelerating PPP-AR is actually limited and usually 5-10 minutes of observations are still needed for a successful PPP initialization. Fortunately, the advanced Galileo E1/E5a/E6 and BeiDou-3 B1I/B3I/B2a signals can form the ionosphere-free wide-lane observables, of which the noise is only 67 and 74 times larger than the original carrier-phase noise, respectively. This would bring about a pronounced improvement on the rapid convergence of PPP-AR. In this study, we hence implemented multi-frequency PPP-AR using such Galileo and BeiDou-3 low-noise combinations. For comparison, PPP-AR based on Galileo E1/E5a/E5b and BeiDou-3 B1I/B3I/B2b was also carried out. Note that we did not form the extra-wide-lane and wide-lane combination observables explicitly, nor did we form ionosphere-free observables to start PPP. Instead, we used uncombined observations in PPP and later mapped the raw ambiguity estimates and their variance-covariance matrix into those of their (extra-)wide- and narrow-lane counterparts for LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) search. In this case, the multi-frequency PPP model could be extendable and more direct. We used multi-GNSS data from 23 stations over 30 days to validate this approach. Precise satellite orbit and clock products calculated by Wuhan University were used for the data processing. We found that both extra-wide-lane and wide-lane phase biases of Galileo and BeiDou-3 satellites were quite stable with a standard deviation of less than 0.01 cycles. Narrow-lane phase biases of Galileo can be estimated precisely with a precision of 0.02 cycles, while 0.01 cycles were also achieved by their BeiDou-3 counterparts. With these phase bias corrections, 16 minutes of observations were required to achieve dual-frequency PPP-AR. However, it took only 10 minutes on average for E1/E5a/E6 and B1I/B3I/B2a PPP-AR whereas 14 minutes for their E1/E5a/E5b and B1I/B3I/B2b counterparts. Moreover, it is found that more satellites could enable better PPP-AR performance; the mean initialization time of E1/E5a/E6 and B1I/B3I/B2a PPP-AR declined to 4 minutes when there were 15 visible Galileo/BeiDou-3 satellites, whereas 7 minutes in case of E1/E5a/E5b and B1I/B3I/B2b PPP-AR. Meanwhile, the positioning accuracy of the first 10 minute of epochs improved from 14 cm, 15 cm and 27 cm for the east, north and up components in case of E1/E5a/E5b and B1I/B3I/B2b PPP-AR to 6 cm, 7 cm and 16 cm in case of E1/E5a/E6 and B1I/B3I/B2a PPP-AR, showing an improvement of almost 50%, Finally, it is worth pointing out that neither Galileo nor BeiDou-3 is fully operational at the moment. We can envision that the full Galileo and BeiDou-3 constellation in the near future will be promising to enable a successful PPP-AR within 5 minutes of observations. We are also designing a vehicle-borne Galileo/BeiDou-3 experiment using the latest Trimble Alloy receiver to test our method, though the firmware has not been upgraded to accommodate BeiDou-3 B2a/b signals.