Probably due wrong pins assigned in the option bits, or IOMUX not configured?
Try with PA1 and PA3, they aren't multiplexed and should work straight away.
LL_GPIO_Init(GPIOA, &(LL_GPIO_InitTypeDef){ LL_GPIO_PIN_1, LL_GPIO_MODE_ALTERNATE, LL_GPIO_SPEED_FREQ_VERY_HIGH, LL_GPIO_OUTPUT_PUSHPULL, LL_GPIO_PULL_NO, LL_GPIO_AF0_SPI1 }); // PA1 = SCK
LL_GPIO_Init(GPIOA, &(LL_GPIO_InitTypeDef){ LL_GPIO_PIN_3, LL_GPIO_MODE_ALTERNATE, LL_GPIO_SPEED_FREQ_VERY_HIGH, LL_GPIO_OUTPUT_PUSHPULL, LL_GPIO_PULL_NO, LL_GPIO_AF10_SPI1 }); // PA3 = MOSI