  The longstanding search for the cosmological model that best describes the
Universe has been made more intriguing since the recent discovery of the Hubble
constant, $H_{0}$, tension observed between the value of $H_{0}$ from the
Cosmic Microwave Background and from type Ia supernovae (SNe Ia). Hence, the
commonly trusted flat $\Lambda$CDM model is under investigation. In this
scenario, cosmography is a very powerful technique to investigate the evolution
of the Universe without any cosmological assumption, thus revealing tensions
between observational data and predictions from cosmological models in a
completely model-independent way. We here employ a robust cosmographic
technique based on an orthogonal logarithmic polynomial expansion of the
luminosity distance to fit quasars (QSOs) alone and QSOs combined with
Gamma-Ray Bursts (GRBs), SNe Ia, and Baryon Acoustic Oscillations. To apply
QSOs and GRBs as probes we use, respectively, the Risaliti-Lusso relation
between ultraviolet and X-ray luminosities and the ``Dainotti GRB 3D relation"
among the rest-frame end time of the X-ray plateau emission, its corresponding
luminosity, and the peak prompt luminosity. We also correct QSOs and GRBs for
selection biases and redshift evolution and we employ both the traditional
Gaussian likelihood and the newly discovered best-fit likelihoods for each
probe investigated. This comprehensive analysis reveals a strong tension ($> 4
\, \sigma$) between our data sets and the flat $\Lambda$CDM model proving the
power of both the cosmographic approach and high-redshift sources, such as QSOs
and GRBs, which can probe the Universe at early epochs.
