im not sure for the material conditions, but Khrushchev hated Stalin and only saw him as an power hungry dictator, this is what he said when stalin died

"Stalin called everyone who didn't agree with him an "enemy of the people." He said that they wanted to restore the old order, and for this purpose, "the enemies of the people" had linked up with the forces of reaction internationally. As a result, several hundred thousand honest people perished. Everyone lived in fear in those days. Everyone expected that at any moment there would be a knock on the door in the middle of the night and that knock on the door would prove fatal ... People not to Stalin's liking were annihilated, honest party members, irreproachable people, loyal and hard workers for our cause who had gone through the school of revolutionary struggle under Lenin's leadership. This was utter and complete arbitrariness. And now is all this to be forgiven and forgotten? Never! "

he did not like Stalin, after Stalin's death there was a power vacuum that had to be filled, the new leadership was Malenkov as the new Chairman of the Council of Ministers, with Beria (he had control over the security services) , Kaganovich, Bulganin, and Vyacheslav Molotov as first vice-chairmen. the soviet Presidium had 10 people with Malenkov and Beria as the more influencial and Khrushchev as the least infuencial.

Malenkov resigned from the secretariat of the Central Committee, This was due to concerns that he was acquiring too much power. The major beneficiary was Khrushchev. His name appeared atop a revised list of secretarie, and he was now in charge of the party.

Beria tried to passed some new reforms using his influence, but he was stopped by the alliance of Khrushchev and Malenkov who fear Beria was gonna coup the government, eventually they convinced Beria's ministers to betray him and Beria lost control of the ministry of interior, then Beria was arrested at a Presidium meeting he was tried and then killed.

After his fall the 2 strongers were Malenkov with the control of the central state apparatus (administration) and the Future Corn-Lord with his power base in the Communist Party. To gain more power Khrushchev presented himself as a down-to-earth activist prepared to take up any challenge (a Proletariat) versus Malenkov who was presented as sophisticated but colorless.

Khrushchev possessed incriminating information on Malenkov, taken from Beria's secret files. At a Central Committee meeting in January 1955, Malenkov was accused of involvement in atrocities, and the committee passed a resolution accusing him of involvement in the Leningrad case, and of facilitating Beria's climb to power. At a meeting of the mostly ceremonial Supreme Soviet the following month, Malenkov was demoted in favour of Bulganin. Malenkov remained in the Presidium as Minister of Electric Power Stations

after this Khrushchev was basically the Leader of the Soviet Union by 1956 and had not opposition until febrary of 1956 when he realised his "secret speech" denouncing Stalin and everything he stand for, Forever Fracturing the CPSU into 2 faction the Reformists and the Stalinists.

JoeySteel has already go in deep as to why was the secret speech bad, but in short it divided the Party from the Masses (killing the Idea of the Party of the Masses) because if the Party took an obvious anti-Stalin position the soviet proletariat would push back against them because they liked Stalin.

Later the last hope for the Soviet Union to not go revisionist, was in 1957 when the alliance of Malenkov, Molotov, and Kaganovich worked to quietly build support to dismiss Khrushchev. They grew in strengh, and eventually threaten Khrushchev position as leader, however they couldnt forced Khrushchev control the Soviet Military through Marshal Zhukov who was a fierce supporter of him and had threathen a Military coup if Khrushchev was deposed.

The three were later expelled from the Central Committee and Presidium. Molotov was sent as Ambassador to Mongolia; the others were sent to head industrial facilities and institutes far from Moscow.

and after that for 6 years Khrushchev was free to do as he pleased since he was the Party Leader, the Commander in Chief and the Presidium Leader, and because of this he was able to continue with his plan of destalinization within the CPSU