One of the earliest examples of Swastika sign in Ukraine is dated from Late Paleolitic period (35.000-11.000 B.C.)  Swastika symbolism represented the sun, which was worshipped and therefore can be found on tools used for various magic purposes.   Such is a wooden carwing fround by archeologists around Mezhyricha region.  Around the same location  a braclet was found which is completelly covered by Swastika-like design.

Wooden statue with solar symbols. Mezhyrich region

Bracelet with Swastika-like design from Mezhyricha

Copper Age (Eneolithic period) The Bronze Age (4.000 - 3.000 B.C.) in Ukraine can be catheorized by few cultures.  The most studied and devoloped is the culture of Trypilia - the people from this culture had very developed argiculture, pottery, domestication, weel carts and large megapolis cities with 3.000 inhabitants.  From stydying the ceramic remains from this time, we discover that sun played a key role in religion of anciet Trypilians, since most of pottery is covered with solar images.

Ceramic plate from Trypilia culture, with Swastika as central element

Ceramic pot from Koshylovtsi area

Swastika plate from Usatove burrial, 3000 B.C.

Pot with Swastika ornament, Usatove type, from Viljan'sky burrial, Dnipro region.

Bronze Age Most noted culture from that period is Zrubna (Sabatynivska) culture (2000-15000B.C.)  It is famed for its burrial sites - Kurgany - a high burrial mount with stone layed chamber inside.  Series of archological discoveries found a number of artifacts with solar symbols on them.  Sucha are pottery  from Poorillia Kurgan, where Swastika is one of the key elements.

Pottery from Poorillia Kugan, 1500 B.C.

Examples of pottery from Zrubna culture.

Swastika was the dominat symbol in Zrubna culture