Intensity-time profiles of solar energetic particles (SEPs) emitted during solar eruptions are shaped by a number of entangled processes. This involves the location of the particle source with respect to the observer, the type, location, and duration of the acceleration process, as well as potentially varying transport effects from the Sun to the observer. Understanding the behavior of these profiles can bring us closer to more reliable space weather forecasting. Using multi-spacecraft observations of SEP events of the early solar cycle 25, we aim to characterize an average SEP profile of the sample. We analyzed 45 SEP events from November 2020–May 2023 provided by the SERPENTINE multi-spacecraft SEP event catalog for ∼100-keV and ∼1-MeV electrons and 25–40 MeV protons, including observations by Solar Orbiter, STEREO A, BepiColombo, Parker Solar Probe, and near-Earth spacecraft (SOHO and Wind), resulting in more than 100 single spacecraft observations. We performed a superposed epoch analysis of the intensity-time profiles, normalized with peak intensity and rise time, separating the events into magnetically well-connected and poorly-connected sectors from the source at the Sun. We also consider the rise and the decay phases separately. We studied the behavior of the mean curves and applied empirical exponential and power law models to fit the mean profiles. We also studied the onset delay between relativistic electrons and protons to validate the potential application of the early arrival of relativistic electrons to forecast the hazardous energetic protons. We find that although the sample contains both impulsive and gradual profiles, they seem to follow the same trend when normalized and are, mostly, better represented by the power law and sometimes by the exponential law. Furthermore, the normalized mean curves for electron and proton profiles do not differ significantly from each other. We conclude that despite having a mixture of impulsive and gradual profiles in the sample, and potentially different contributions from flare and shock acceleration, a representative average SEP profile can be determined. The similarity of the mean normalized SEP profiles of high-energy electrons and protons supports the use of the early alert of relativistic electrons to forecast the later-arriving energetic protons and suggests that the forecasting scheme should work better with high-energy electrons.