Manned Mars missions planned in the near future of very low solar activity period and hence higher than acceptable radiation doses due mainly to the Galactic Cosmic Rays (GCR), would require special techniques and technological development for maintaining the good health of the astronauts. The present study is an attempt to make an assessment and characterise the coming years in terms of solar activity and space radiation environment especially due to the abundance of highly energetic heavy ions (known as HZE charged particles). These HZE particle fluxes constitute a major hazard to the astronauts and also to the critical electronic components of the spacecraft. Recent data on the HZE species (from B to Ni) obtained from ACE spacecraft shows a clear enhancement of the particle fluxes between the solar cycle 23 and solar cycle 24 (~between SSN peaks 2002 and 2014) due to the persisting low sunspot numbers of the latter cycle. The peak values of these cosmic ray fluxes occur with a time lag of about a year of the corresponding minimum value of the sunspots of a particular 11-year cycle which is pseudo-periodic in nature. This is demonstrated by the Fourier and Wavelet transform analyses of the long duration (1700–2018) yearly mean sunspot number data. The same time series data is also used to train a Hybrid Regression Neural Network (HRNN) model to generate the predicted yearly mean sunspot numbers for the solar cycle 25 (~2019–2031). The wavelet analysis of this new series of annual sunspot numbers including the predictions up to the end of 2031 shows a clear trend of continuation of the low solar activity and hence continuation of very high HZE fluxes prevailing in Solar cycle 24 into the solar cycle 25 and perhaps beyond.