This answer will assume that the huge solar storm sought by the OP can be obtained through natural processes. The most probable candidate for giant solar storms are coronal mass ejections.
Coronal mass ejections release huge quantities of matter and electromagnetic radiation into space above the Sun's surface, either near the corona (sometimes called a solar prominence), or farther into the planetary system, or beyond (interplanetary CME). The ejected material is a plasma consisting primarily of electrons and protons. While solar flares are very fast, CMEs are relatively slow.
CMEs occur frequently and carry a reasonable amount of mass at quite high velocities. Although there is a wide range of velocities for CMEs.
Coronal mass ejections reach velocities from 20 to 3,200 km/s (12 to 1,988 mi/s) with an average speed of 489 km/s (304 mi/s), based on SOHO/LASCO measurements between 1996 and 2003. These speeds correspond to transit times from the Sun out to the mean radius of Earth's orbit of about 13 hours to 86 days (extremes), with about 3.5 days as the average. The average mass ejected is 1.6×1012 kg (3.5×1012 lb). However, the estimated mass values for CMEs are only lower limits, because coronagraph measurements provide only two-dimensional data. The frequency of ejections depends on the phase of the solar cycle: from about one every fifth day near the solar minimum to 3.5 per day near the solar maximum.
The destructive power of CMEs can be gauged from understanding what happened with the first discovery of CMEs in 1859. This is also known as the Carrington Event.
The largest recorded geomagnetic perturbation, resulting presumably from a CME, coincided with the first-observed solar flare on 1 September 1859, and is now referred to as the Carrington Event, or the solar storm of 1859. The flare and the associated sunspots were visible to the naked eye (both as the flare itself appearing on a projection of the Sun on a screen and as an aggregate brightening of the solar disc), and the flare was independently observed by English astronomers R. C. Carrington and R. Hodgson. The geomagnetic storm was observed with the recording magnetograph at Kew Gardens. The same instrument recorded a crochet, an instantaneous perturbation of Earth's ionosphere by ionizing soft X-rays. This could not easily be understood at the time because it predated the discovery of X-rays by Röntgen and the recognition of the ionosphere by Kennelly and Heaviside. The storm took down parts of the recently created US telegraph network, starting fires and shocking some telegraph operators.
Apparently during the Carrington Event the telegraph network could also work without needing to be powered up.
A Carrington-class CME missed hitting the Earth in 2014. Now the first CME to be detected as such was in 1971. While we know there were Carrington-class CMEs in 1859 and 2014, this suggests there might have been other Carrington-class CMEs which, like the 2014 event, may have missed the Earth.
Extrapolating from this data, it is possible to assume that Carrington-class CMEs occur with a frequency of approximately one hundred and sixty years. However, this might be increased to a frequency of approximately of, say, seventy-five years (this assumes there was an undetected Carrington CME somewhere between 1859 and 2104). Although the Carrington frequency of 160 years is our best estimate based on known data (this is the most conservative manner for making an estimate).
Considering that CMEs are frequent, varying from one every 3.5 days to once per five days, and if Carrington-class CMEs happen on average once in 160 years, to extrapolate to CMEs with magnitudes two to three orders of magnitude greater than Carrington-class CME this will be the result of blind chance itself.
Such super-Carrington-class CMEs can be CMEs that occur with a lower probability. For example, a super-Carrington-class CME that is three orders of magnitude could occur once in a million years. Certainly CMEs display considerable variability and this variability does not exclude the possibility and the probability that there will be super-Carrington-class CMEs.
This information about recent CME events indicates that CMEs could easily generate massive solar storms.
On 1 August 2010, during solar cycle 24, scientists at the
Harvard-Smithsonian Center for Astrophysics (CfA) observed a series of
four large CMEs emanating from the Earth-facing hemisphere of the Sun.
The initial CME was generated by an eruption on 1 August that was
associated with NOAA Active Region 1092, which was large enough to be
seen without the aid of a solar telescope. The event produced
significant aurorae on Earth three days later.
On 23 July 2012, a massive, and potentially damaging, solar superstorm
(solar flare, CME, solar EMP) barely missed Earth, according to
NASA. There is an estimated 12% chance of a similar event
hitting Earth between 2012 and 2022.
On 31 August 2012 a CME connected with Earth's magnetic environment,
or magnetosphere, with a glancing blow causing aurora to appear on the
night of 3 September. Geomagnetic storming reached the G2
(Kp=6) level on NOAA's Space Weather Prediction Center scale of
All of this suggests that CMEs are a more than probable source of huge solar storms. Since low probability events are happening all the time, so say the statisticians, then low probability events like Super-Carrington-class CMEs can happen and will happen.